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Simplifying 7x + -2x(4x + -3) = 8(x + -9) + -30 Reorder the terms: 7x + -2x(-3 + 4x) = 8(x + -9) + -30 7x + (-3 * -2x + 4x * -2x) = 8(x + -9) + -30 7x + (6x + -8x2) = 8(x + -9) + -30 Combine like terms: 7x + 6x = 13x 13x + -8x2 = 8(x + -9) + -30 Reorder the terms: 13x + -8x2 = 8(-9 + x) + -30 13x + -8x2 = (-9 * 8 + x * 8) + -30 13x + -8x2 = (-72 + 8x) + -30 Reorder the terms: 13x + -8x2 = -72 + -30 + 8x Combine like terms: -72 + -30 = -102 13x + -8x2 = -102 + 8x Solving 13x + -8x2 = -102 + 8x Solving for variable 'x'. Reorder the terms: 102 + 13x + -8x + -8x2 = -102 + 8x + 102 + -8x Combine like terms: 13x + -8x = 5x 102 + 5x + -8x2 = -102 + 8x + 102 + -8x Reorder the terms: 102 + 5x + -8x2 = -102 + 102 + 8x + -8x Combine like terms: -102 + 102 = 0 102 + 5x + -8x2 = 0 + 8x + -8x 102 + 5x + -8x2 = 8x + -8x Combine like terms: 8x + -8x = 0 102 + 5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -12.75 + -0.625x + x2 = 0 Move the constant term to the right: Add '12.75' to each side of the equation. -12.75 + -0.625x + 12.75 + x2 = 0 + 12.75 Reorder the terms: -12.75 + 12.75 + -0.625x + x2 = 0 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + -0.625x + x2 = 0 + 12.75 -0.625x + x2 = 0 + 12.75 Combine like terms: 0 + 12.75 = 12.75 -0.625x + x2 = 12.75 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 12.75 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 12.75 + 0.09765625 Combine like terms: 12.75 + 0.09765625 = 12.84765625 0.09765625 + -0.625x + x2 = 12.84765625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 12.84765625 Calculate the square root of the right side: 3.58436274 Break this problem into two subproblems by setting (x + -0.3125) equal to 3.58436274 and -3.58436274.Subproblem 1
x + -0.3125 = 3.58436274 Simplifying x + -0.3125 = 3.58436274 Reorder the terms: -0.3125 + x = 3.58436274 Solving -0.3125 + x = 3.58436274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 3.58436274 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 3.58436274 + 0.3125 x = 3.58436274 + 0.3125 Combine like terms: 3.58436274 + 0.3125 = 3.89686274 x = 3.89686274 Simplifying x = 3.89686274Subproblem 2
x + -0.3125 = -3.58436274 Simplifying x + -0.3125 = -3.58436274 Reorder the terms: -0.3125 + x = -3.58436274 Solving -0.3125 + x = -3.58436274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -3.58436274 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -3.58436274 + 0.3125 x = -3.58436274 + 0.3125 Combine like terms: -3.58436274 + 0.3125 = -3.27186274 x = -3.27186274 Simplifying x = -3.27186274Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.89686274, -3.27186274}
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