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Simplifying 16x2 + 17x + -15 = 0 Reorder the terms: -15 + 17x + 16x2 = 0 Solving -15 + 17x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + 1.0625x + x2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + 1.0625x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + 1.0625x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + 1.0625x + x2 = 0 + 0.9375 1.0625x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 1.0625x + x2 = 0.9375 The x term is 1.0625x. Take half its coefficient (0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. 1.0625x + 0.2822265625 + x2 = 0.9375 + 0.2822265625 Reorder the terms: 0.2822265625 + 1.0625x + x2 = 0.9375 + 0.2822265625 Combine like terms: 0.9375 + 0.2822265625 = 1.2197265625 0.2822265625 + 1.0625x + x2 = 1.2197265625 Factor a perfect square on the left side: (x + 0.53125)(x + 0.53125) = 1.2197265625 Calculate the square root of the right side: 1.104412315 Break this problem into two subproblems by setting (x + 0.53125) equal to 1.104412315 and -1.104412315.Subproblem 1
x + 0.53125 = 1.104412315 Simplifying x + 0.53125 = 1.104412315 Reorder the terms: 0.53125 + x = 1.104412315 Solving 0.53125 + x = 1.104412315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + x = 1.104412315 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + x = 1.104412315 + -0.53125 x = 1.104412315 + -0.53125 Combine like terms: 1.104412315 + -0.53125 = 0.573162315 x = 0.573162315 Simplifying x = 0.573162315Subproblem 2
x + 0.53125 = -1.104412315 Simplifying x + 0.53125 = -1.104412315 Reorder the terms: 0.53125 + x = -1.104412315 Solving 0.53125 + x = -1.104412315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + x = -1.104412315 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + x = -1.104412315 + -0.53125 x = -1.104412315 + -0.53125 Combine like terms: -1.104412315 + -0.53125 = -1.635662315 x = -1.635662315 Simplifying x = -1.635662315Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.573162315, -1.635662315}
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