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Simplifying -7x2 + 12x = -12 + 2x Reorder the terms: 12x + -7x2 = -12 + 2x Solving 12x + -7x2 = -12 + 2x Solving for variable 'x'. Reorder the terms: 12 + 12x + -2x + -7x2 = -12 + 2x + 12 + -2x Combine like terms: 12x + -2x = 10x 12 + 10x + -7x2 = -12 + 2x + 12 + -2x Reorder the terms: 12 + 10x + -7x2 = -12 + 12 + 2x + -2x Combine like terms: -12 + 12 = 0 12 + 10x + -7x2 = 0 + 2x + -2x 12 + 10x + -7x2 = 2x + -2x Combine like terms: 2x + -2x = 0 12 + 10x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.714285714 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -1.428571429x + 1.714285714 + x2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -1.428571429x + x2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -1.428571429x + x2 = 0 + 1.714285714 -1.428571429x + x2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -1.428571429x + x2 = 1.714285714 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 1.714285714 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 1.714285714 + 0.5102040819 Combine like terms: 1.714285714 + 0.5102040819 = 2.2244897959 0.5102040819 + -1.428571429x + x2 = 2.2244897959 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 2.2244897959 Calculate the square root of the right side: 1.491472358 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 1.491472358 and -1.491472358.Subproblem 1
x + -0.7142857145 = 1.491472358 Simplifying x + -0.7142857145 = 1.491472358 Reorder the terms: -0.7142857145 + x = 1.491472358 Solving -0.7142857145 + x = 1.491472358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 1.491472358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 1.491472358 + 0.7142857145 x = 1.491472358 + 0.7142857145 Combine like terms: 1.491472358 + 0.7142857145 = 2.2057580725 x = 2.2057580725 Simplifying x = 2.2057580725Subproblem 2
x + -0.7142857145 = -1.491472358 Simplifying x + -0.7142857145 = -1.491472358 Reorder the terms: -0.7142857145 + x = -1.491472358 Solving -0.7142857145 + x = -1.491472358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -1.491472358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -1.491472358 + 0.7142857145 x = -1.491472358 + 0.7142857145 Combine like terms: -1.491472358 + 0.7142857145 = -0.7771866435 x = -0.7771866435 Simplifying x = -0.7771866435Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2057580725, -0.7771866435}
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