Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]enter your response here (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Question

Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]enter your response here ​(Type an integer or a simplified fraction. Use a comma to separate answers as​ needed.)

BlackTom AI · Accepted Answer

The problem asks to solve the quadratic equation 63x − 36x^2 = 0 by factoring and fill in two blanks for the solutions.
First, reorder terms to standard form or factor directly: −36x^2 + 63x = 0. Factor out the greatest common factor, which is 9x, from both terms: 9x(7 − 4x) = 0.
Now apply the zero-product property: a product equals zero if and only if at least one factor is zero. This gives two equations: 9x = 0 and 7 − 4x = 0.
From 9x = 0, we obtain x = 0. This provides the first solution for the first blank.
From 7 − 4x = 0, we solve for x by moving 7 to the other side and then dividing by −4: −4x = −7 → x = 7/4. This supplies the second solution for the second blank.
Check the solutions quickly by substitution: plug x = 0 into the original equation to see 0 − 0 = 0, which holds. Plug x = 7/4: 63(7/4) − 36(49/16) = (441/4) − (1764/16) = (441/4) − (441/4) = 0, which also holds.
Therefore, the two solutions to the equation are x = 0 and x = 7/4, and they correspond to the two blanks in the order requested by the prompt.

Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]enter your response here (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)多项填空题

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Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]enter your response here ​(Type an integer or a simplified fraction. Use a comma to separate answers as​ needed.)多项填空题