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Simplifying 8x(8x) + -15x + -2 = 0 Remove parenthesis around (8x) 8x * 8x + -15x + -2 = 0 Reorder the terms for easier multiplication: 8 * 8x * x + -15x + -2 = 0 Multiply 8 * 8 64x * x + -15x + -2 = 0 Multiply x * x 64x2 + -15x + -2 = 0 Reorder the terms: -2 + -15x + 64x2 = 0 Solving -2 + -15x + 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'. -0.03125 + -0.234375x + x2 = 0 Move the constant term to the right: Add '0.03125' to each side of the equation. -0.03125 + -0.234375x + 0.03125 + x2 = 0 + 0.03125 Reorder the terms: -0.03125 + 0.03125 + -0.234375x + x2 = 0 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + -0.234375x + x2 = 0 + 0.03125 -0.234375x + x2 = 0 + 0.03125 Combine like terms: 0 + 0.03125 = 0.03125 -0.234375x + x2 = 0.03125 The x term is -0.234375x. Take half its coefficient (-0.1171875). Square it (0.01373291016) and add it to both sides. Add '0.01373291016' to each side of the equation. -0.234375x + 0.01373291016 + x2 = 0.03125 + 0.01373291016 Reorder the terms: 0.01373291016 + -0.234375x + x2 = 0.03125 + 0.01373291016 Combine like terms: 0.03125 + 0.01373291016 = 0.04498291016 0.01373291016 + -0.234375x + x2 = 0.04498291016 Factor a perfect square on the left side: (x + -0.1171875)(x + -0.1171875) = 0.04498291016 Calculate the square root of the right side: 0.212091749 Break this problem into two subproblems by setting (x + -0.1171875) equal to 0.212091749 and -0.212091749.Subproblem 1
x + -0.1171875 = 0.212091749 Simplifying x + -0.1171875 = 0.212091749 Reorder the terms: -0.1171875 + x = 0.212091749 Solving -0.1171875 + x = 0.212091749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1171875' to each side of the equation. -0.1171875 + 0.1171875 + x = 0.212091749 + 0.1171875 Combine like terms: -0.1171875 + 0.1171875 = 0.0000000 0.0000000 + x = 0.212091749 + 0.1171875 x = 0.212091749 + 0.1171875 Combine like terms: 0.212091749 + 0.1171875 = 0.329279249 x = 0.329279249 Simplifying x = 0.329279249Subproblem 2
x + -0.1171875 = -0.212091749 Simplifying x + -0.1171875 = -0.212091749 Reorder the terms: -0.1171875 + x = -0.212091749 Solving -0.1171875 + x = -0.212091749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1171875' to each side of the equation. -0.1171875 + 0.1171875 + x = -0.212091749 + 0.1171875 Combine like terms: -0.1171875 + 0.1171875 = 0.0000000 0.0000000 + x = -0.212091749 + 0.1171875 x = -0.212091749 + 0.1171875 Combine like terms: -0.212091749 + 0.1171875 = -0.094904249 x = -0.094904249 Simplifying x = -0.094904249Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.329279249, -0.094904249}
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