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Simplifying -16x2 + -15x + 207 = 0 Reorder the terms: 207 + -15x + -16x2 = 0 Solving 207 + -15x + -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'. -12.9375 + 0.9375x + x2 = 0 Move the constant term to the right: Add '12.9375' to each side of the equation. -12.9375 + 0.9375x + 12.9375 + x2 = 0 + 12.9375 Reorder the terms: -12.9375 + 12.9375 + 0.9375x + x2 = 0 + 12.9375 Combine like terms: -12.9375 + 12.9375 = 0.0000 0.0000 + 0.9375x + x2 = 0 + 12.9375 0.9375x + x2 = 0 + 12.9375 Combine like terms: 0 + 12.9375 = 12.9375 0.9375x + x2 = 12.9375 The x term is 0.9375x. Take half its coefficient (0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. 0.9375x + 0.2197265625 + x2 = 12.9375 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375x + x2 = 12.9375 + 0.2197265625 Combine like terms: 12.9375 + 0.2197265625 = 13.1572265625 0.2197265625 + 0.9375x + x2 = 13.1572265625 Factor a perfect square on the left side: (x + 0.46875)(x + 0.46875) = 13.1572265625 Calculate the square root of the right side: 3.627289148 Break this problem into two subproblems by setting (x + 0.46875) equal to 3.627289148 and -3.627289148.Subproblem 1
x + 0.46875 = 3.627289148 Simplifying x + 0.46875 = 3.627289148 Reorder the terms: 0.46875 + x = 3.627289148 Solving 0.46875 + x = 3.627289148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + x = 3.627289148 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + x = 3.627289148 + -0.46875 x = 3.627289148 + -0.46875 Combine like terms: 3.627289148 + -0.46875 = 3.158539148 x = 3.158539148 Simplifying x = 3.158539148Subproblem 2
x + 0.46875 = -3.627289148 Simplifying x + 0.46875 = -3.627289148 Reorder the terms: 0.46875 + x = -3.627289148 Solving 0.46875 + x = -3.627289148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + x = -3.627289148 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + x = -3.627289148 + -0.46875 x = -3.627289148 + -0.46875 Combine like terms: -3.627289148 + -0.46875 = -4.096039148 x = -4.096039148 Simplifying x = -4.096039148Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.158539148, -4.096039148}
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