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Simplifying 15 = 8x(8x) + -14x Remove parenthesis around (8x) 15 = 8x * 8x + -14x Reorder the terms for easier multiplication: 15 = 8 * 8x * x + -14x Multiply 8 * 8 15 = 64x * x + -14x Multiply x * x 15 = 64x2 + -14x Reorder the terms: 15 = -14x + 64x2 Solving 15 = -14x + 64x2 Solving for variable 'x'. Reorder the terms: 15 + 14x + -64x2 = -14x + 14x + 64x2 + -64x2 Combine like terms: -14x + 14x = 0 15 + 14x + -64x2 = 0 + 64x2 + -64x2 15 + 14x + -64x2 = 64x2 + -64x2 Combine like terms: 64x2 + -64x2 = 0 15 + 14x + -64x2 = 0 Begin completing the square. Divide all terms by -64 the coefficient of the squared term: Divide each side by '-64'. -0.234375 + -0.21875x + x2 = 0 Move the constant term to the right: Add '0.234375' to each side of the equation. -0.234375 + -0.21875x + 0.234375 + x2 = 0 + 0.234375 Reorder the terms: -0.234375 + 0.234375 + -0.21875x + x2 = 0 + 0.234375 Combine like terms: -0.234375 + 0.234375 = 0.000000 0.000000 + -0.21875x + x2 = 0 + 0.234375 -0.21875x + x2 = 0 + 0.234375 Combine like terms: 0 + 0.234375 = 0.234375 -0.21875x + x2 = 0.234375 The x term is -0.21875x. Take half its coefficient (-0.109375). Square it (0.01196289063) and add it to both sides. Add '0.01196289063' to each side of the equation. -0.21875x + 0.01196289063 + x2 = 0.234375 + 0.01196289063 Reorder the terms: 0.01196289063 + -0.21875x + x2 = 0.234375 + 0.01196289063 Combine like terms: 0.234375 + 0.01196289063 = 0.24633789063 0.01196289063 + -0.21875x + x2 = 0.24633789063 Factor a perfect square on the left side: (x + -0.109375)(x + -0.109375) = 0.24633789063 Calculate the square root of the right side: 0.49632438 Break this problem into two subproblems by setting (x + -0.109375) equal to 0.49632438 and -0.49632438.Subproblem 1
x + -0.109375 = 0.49632438 Simplifying x + -0.109375 = 0.49632438 Reorder the terms: -0.109375 + x = 0.49632438 Solving -0.109375 + x = 0.49632438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.109375' to each side of the equation. -0.109375 + 0.109375 + x = 0.49632438 + 0.109375 Combine like terms: -0.109375 + 0.109375 = 0.000000 0.000000 + x = 0.49632438 + 0.109375 x = 0.49632438 + 0.109375 Combine like terms: 0.49632438 + 0.109375 = 0.60569938 x = 0.60569938 Simplifying x = 0.60569938Subproblem 2
x + -0.109375 = -0.49632438 Simplifying x + -0.109375 = -0.49632438 Reorder the terms: -0.109375 + x = -0.49632438 Solving -0.109375 + x = -0.49632438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.109375' to each side of the equation. -0.109375 + 0.109375 + x = -0.49632438 + 0.109375 Combine like terms: -0.109375 + 0.109375 = 0.000000 0.000000 + x = -0.49632438 + 0.109375 x = -0.49632438 + 0.109375 Combine like terms: -0.49632438 + 0.109375 = -0.38694938 x = -0.38694938 Simplifying x = -0.38694938Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.60569938, -0.38694938}
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