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Simplifying 4x(3x + 2) + -1x = -8x + 11 Reorder the terms: 4x(2 + 3x) + -1x = -8x + 11 (2 * 4x + 3x * 4x) + -1x = -8x + 11 (8x + 12x2) + -1x = -8x + 11 Reorder the terms: 8x + -1x + 12x2 = -8x + 11 Combine like terms: 8x + -1x = 7x 7x + 12x2 = -8x + 11 Reorder the terms: 7x + 12x2 = 11 + -8x Solving 7x + 12x2 = 11 + -8x Solving for variable 'x'. Reorder the terms: -11 + 7x + 8x + 12x2 = 11 + -8x + -11 + 8x Combine like terms: 7x + 8x = 15x -11 + 15x + 12x2 = 11 + -8x + -11 + 8x Reorder the terms: -11 + 15x + 12x2 = 11 + -11 + -8x + 8x Combine like terms: 11 + -11 = 0 -11 + 15x + 12x2 = 0 + -8x + 8x -11 + 15x + 12x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -11 + 15x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.9166666667 + 1.25x + x2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + 1.25x + 0.9166666667 + x2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + 1.25x + x2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + 1.25x + x2 = 0 + 0.9166666667 1.25x + x2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 1.25x + x2 = 0.9166666667 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 0.9166666667 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 0.9166666667 + 0.390625 Combine like terms: 0.9166666667 + 0.390625 = 1.3072916667 0.390625 + 1.25x + x2 = 1.3072916667 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 1.3072916667 Calculate the square root of the right side: 1.143368561 Break this problem into two subproblems by setting (x + 0.625) equal to 1.143368561 and -1.143368561.Subproblem 1
x + 0.625 = 1.143368561 Simplifying x + 0.625 = 1.143368561 Reorder the terms: 0.625 + x = 1.143368561 Solving 0.625 + x = 1.143368561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.143368561 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.143368561 + -0.625 x = 1.143368561 + -0.625 Combine like terms: 1.143368561 + -0.625 = 0.518368561 x = 0.518368561 Simplifying x = 0.518368561Subproblem 2
x + 0.625 = -1.143368561 Simplifying x + 0.625 = -1.143368561 Reorder the terms: 0.625 + x = -1.143368561 Solving 0.625 + x = -1.143368561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.143368561 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.143368561 + -0.625 x = -1.143368561 + -0.625 Combine like terms: -1.143368561 + -0.625 = -1.768368561 x = -1.768368561 Simplifying x = -1.768368561Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.518368561, -1.768368561}
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