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Simplifying (8x)(8x) + 10x + -7 = 0 Remove parenthesis around (8x) 8x(8x) + 10x + -7 = 0 Remove parenthesis around (8x) 8x * 8x + 10x + -7 = 0 Reorder the terms for easier multiplication: 8 * 8x * x + 10x + -7 = 0 Multiply 8 * 8 64x * x + 10x + -7 = 0 Multiply x * x 64x2 + 10x + -7 = 0 Reorder the terms: -7 + 10x + 64x2 = 0 Solving -7 + 10x + 64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.109375 + 0.15625x + x2 = 0 Move the constant term to the right: Add '0.109375' to each side of the equation. -0.109375 + 0.15625x + 0.109375 + x2 = 0 + 0.109375 Reorder the terms: -0.109375 + 0.109375 + 0.15625x + x2 = 0 + 0.109375 Combine like terms: -0.109375 + 0.109375 = 0.000000 0.000000 + 0.15625x + x2 = 0 + 0.109375 0.15625x + x2 = 0 + 0.109375 Combine like terms: 0 + 0.109375 = 0.109375 0.15625x + x2 = 0.109375 The x term is 0.15625x. Take half its coefficient (0.078125). Square it (0.006103515625) and add it to both sides. Add '0.006103515625' to each side of the equation. 0.15625x + 0.006103515625 + x2 = 0.109375 + 0.006103515625 Reorder the terms: 0.006103515625 + 0.15625x + x2 = 0.109375 + 0.006103515625 Combine like terms: 0.109375 + 0.006103515625 = 0.115478515625 0.006103515625 + 0.15625x + x2 = 0.115478515625 Factor a perfect square on the left side: (x + 0.078125)(x + 0.078125) = 0.115478515625 Calculate the square root of the right side: 0.3398213 Break this problem into two subproblems by setting (x + 0.078125) equal to 0.3398213 and -0.3398213.Subproblem 1
x + 0.078125 = 0.3398213 Simplifying x + 0.078125 = 0.3398213 Reorder the terms: 0.078125 + x = 0.3398213 Solving 0.078125 + x = 0.3398213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.078125' to each side of the equation. 0.078125 + -0.078125 + x = 0.3398213 + -0.078125 Combine like terms: 0.078125 + -0.078125 = 0.000000 0.000000 + x = 0.3398213 + -0.078125 x = 0.3398213 + -0.078125 Combine like terms: 0.3398213 + -0.078125 = 0.2616963 x = 0.2616963 Simplifying x = 0.2616963Subproblem 2
x + 0.078125 = -0.3398213 Simplifying x + 0.078125 = -0.3398213 Reorder the terms: 0.078125 + x = -0.3398213 Solving 0.078125 + x = -0.3398213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.078125' to each side of the equation. 0.078125 + -0.078125 + x = -0.3398213 + -0.078125 Combine like terms: 0.078125 + -0.078125 = 0.000000 0.000000 + x = -0.3398213 + -0.078125 x = -0.3398213 + -0.078125 Combine like terms: -0.3398213 + -0.078125 = -0.4179463 x = -0.4179463 Simplifying x = -0.4179463Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2616963, -0.4179463}
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