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Simplifying 7x * 5x + -1 = 12 * 2x + 2 Reorder the terms for easier multiplication: 7 * 5x * x + -1 = 12 * 2x + 2 Multiply 7 * 5 35x * x + -1 = 12 * 2x + 2 Multiply x * x 35x2 + -1 = 12 * 2x + 2 Reorder the terms: -1 + 35x2 = 12 * 2x + 2 Multiply 12 * 2 -1 + 35x2 = 24x + 2 Reorder the terms: -1 + 35x2 = 2 + 24x Solving -1 + 35x2 = 2 + 24x Solving for variable 'x'. Reorder the terms: -1 + -2 + -24x + 35x2 = 2 + 24x + -2 + -24x Combine like terms: -1 + -2 = -3 -3 + -24x + 35x2 = 2 + 24x + -2 + -24x Reorder the terms: -3 + -24x + 35x2 = 2 + -2 + 24x + -24x Combine like terms: 2 + -2 = 0 -3 + -24x + 35x2 = 0 + 24x + -24x -3 + -24x + 35x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -3 + -24x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.08571428571 + -0.6857142857x + x2 = 0 Move the constant term to the right: Add '0.08571428571' to each side of the equation. -0.08571428571 + -0.6857142857x + 0.08571428571 + x2 = 0 + 0.08571428571 Reorder the terms: -0.08571428571 + 0.08571428571 + -0.6857142857x + x2 = 0 + 0.08571428571 Combine like terms: -0.08571428571 + 0.08571428571 = 0.00000000000 0.00000000000 + -0.6857142857x + x2 = 0 + 0.08571428571 -0.6857142857x + x2 = 0 + 0.08571428571 Combine like terms: 0 + 0.08571428571 = 0.08571428571 -0.6857142857x + x2 = 0.08571428571 The x term is -0.6857142857x. Take half its coefficient (-0.3428571429). Square it (0.1175510204) and add it to both sides. Add '0.1175510204' to each side of the equation. -0.6857142857x + 0.1175510204 + x2 = 0.08571428571 + 0.1175510204 Reorder the terms: 0.1175510204 + -0.6857142857x + x2 = 0.08571428571 + 0.1175510204 Combine like terms: 0.08571428571 + 0.1175510204 = 0.20326530611 0.1175510204 + -0.6857142857x + x2 = 0.20326530611 Factor a perfect square on the left side: (x + -0.3428571429)(x + -0.3428571429) = 0.20326530611 Calculate the square root of the right side: 0.450849538 Break this problem into two subproblems by setting (x + -0.3428571429) equal to 0.450849538 and -0.450849538.Subproblem 1
x + -0.3428571429 = 0.450849538 Simplifying x + -0.3428571429 = 0.450849538 Reorder the terms: -0.3428571429 + x = 0.450849538 Solving -0.3428571429 + x = 0.450849538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3428571429' to each side of the equation. -0.3428571429 + 0.3428571429 + x = 0.450849538 + 0.3428571429 Combine like terms: -0.3428571429 + 0.3428571429 = 0.0000000000 0.0000000000 + x = 0.450849538 + 0.3428571429 x = 0.450849538 + 0.3428571429 Combine like terms: 0.450849538 + 0.3428571429 = 0.7937066809 x = 0.7937066809 Simplifying x = 0.7937066809Subproblem 2
x + -0.3428571429 = -0.450849538 Simplifying x + -0.3428571429 = -0.450849538 Reorder the terms: -0.3428571429 + x = -0.450849538 Solving -0.3428571429 + x = -0.450849538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3428571429' to each side of the equation. -0.3428571429 + 0.3428571429 + x = -0.450849538 + 0.3428571429 Combine like terms: -0.3428571429 + 0.3428571429 = 0.0000000000 0.0000000000 + x = -0.450849538 + 0.3428571429 x = -0.450849538 + 0.3428571429 Combine like terms: -0.450849538 + 0.3428571429 = -0.1079923951 x = -0.1079923951 Simplifying x = -0.1079923951Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7937066809, -0.1079923951}
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