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Simplifying (-12x2 + 9x) + -1(7x2 + 10x + -1) = 0 Reorder the terms: (9x + -12x2) + -1(7x2 + 10x + -1) = 0 Remove parenthesis around (9x + -12x2) 9x + -12x2 + -1(7x2 + 10x + -1) = 0 Reorder the terms: 9x + -12x2 + -1(-1 + 10x + 7x2) = 0 9x + -12x2 + (-1 * -1 + 10x * -1 + 7x2 * -1) = 0 9x + -12x2 + (1 + -10x + -7x2) = 0 Reorder the terms: 1 + 9x + -10x + -12x2 + -7x2 = 0 Combine like terms: 9x + -10x = -1x 1 + -1x + -12x2 + -7x2 = 0 Combine like terms: -12x2 + -7x2 = -19x2 1 + -1x + -19x2 = 0 Solving 1 + -1x + -19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. -0.05263157895 + 0.05263157895x + x2 = 0 Move the constant term to the right: Add '0.05263157895' to each side of the equation. -0.05263157895 + 0.05263157895x + 0.05263157895 + x2 = 0 + 0.05263157895 Reorder the terms: -0.05263157895 + 0.05263157895 + 0.05263157895x + x2 = 0 + 0.05263157895 Combine like terms: -0.05263157895 + 0.05263157895 = 0.00000000000 0.00000000000 + 0.05263157895x + x2 = 0 + 0.05263157895 0.05263157895x + x2 = 0 + 0.05263157895 Combine like terms: 0 + 0.05263157895 = 0.05263157895 0.05263157895x + x2 = 0.05263157895 The x term is 0.05263157895x. Take half its coefficient (0.02631578948). Square it (0.0006925207760) and add it to both sides. Add '0.0006925207760' to each side of the equation. 0.05263157895x + 0.0006925207760 + x2 = 0.05263157895 + 0.0006925207760 Reorder the terms: 0.0006925207760 + 0.05263157895x + x2 = 0.05263157895 + 0.0006925207760 Combine like terms: 0.05263157895 + 0.0006925207760 = 0.053324099726 0.0006925207760 + 0.05263157895x + x2 = 0.053324099726 Factor a perfect square on the left side: (x + 0.02631578948)(x + 0.02631578948) = 0.053324099726 Calculate the square root of the right side: 0.230920115 Break this problem into two subproblems by setting (x + 0.02631578948) equal to 0.230920115 and -0.230920115.Subproblem 1
x + 0.02631578948 = 0.230920115 Simplifying x + 0.02631578948 = 0.230920115 Reorder the terms: 0.02631578948 + x = 0.230920115 Solving 0.02631578948 + x = 0.230920115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02631578948' to each side of the equation. 0.02631578948 + -0.02631578948 + x = 0.230920115 + -0.02631578948 Combine like terms: 0.02631578948 + -0.02631578948 = 0.00000000000 0.00000000000 + x = 0.230920115 + -0.02631578948 x = 0.230920115 + -0.02631578948 Combine like terms: 0.230920115 + -0.02631578948 = 0.20460432552 x = 0.20460432552 Simplifying x = 0.20460432552Subproblem 2
x + 0.02631578948 = -0.230920115 Simplifying x + 0.02631578948 = -0.230920115 Reorder the terms: 0.02631578948 + x = -0.230920115 Solving 0.02631578948 + x = -0.230920115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02631578948' to each side of the equation. 0.02631578948 + -0.02631578948 + x = -0.230920115 + -0.02631578948 Combine like terms: 0.02631578948 + -0.02631578948 = 0.00000000000 0.00000000000 + x = -0.230920115 + -0.02631578948 x = -0.230920115 + -0.02631578948 Combine like terms: -0.230920115 + -0.02631578948 = -0.25723590448 x = -0.25723590448 Simplifying x = -0.25723590448Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.20460432552, -0.25723590448}
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