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Simplifying 0 = -16x2 + 15x + 6 Reorder the terms: 0 = 6 + 15x + -16x2 Solving 0 = 6 + 15x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -15x + 16x2 = 6 + 15x + -16x2 + -6 + -15x + 16x2 Reorder the terms: -6 + -15x + 16x2 = 6 + -6 + 15x + -15x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -6 + -15x + 16x2 = 0 + 15x + -15x + -16x2 + 16x2 -6 + -15x + 16x2 = 15x + -15x + -16x2 + 16x2 Combine like terms: 15x + -15x = 0 -6 + -15x + 16x2 = 0 + -16x2 + 16x2 -6 + -15x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -6 + -15x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.375 + -0.9375x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.9375x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.9375x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.9375x + x2 = 0 + 0.375 -0.9375x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.9375x + x2 = 0.375 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 = 0.375 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375x + x2 = 0.375 + 0.2197265625 Combine like terms: 0.375 + 0.2197265625 = 0.5947265625 0.2197265625 + -0.9375x + x2 = 0.5947265625 Factor a perfect square on the left side: (x + -0.46875)(x + -0.46875) = 0.5947265625 Calculate the square root of the right side: 0.771185167 Break this problem into two subproblems by setting (x + -0.46875) equal to 0.771185167 and -0.771185167.Subproblem 1
x + -0.46875 = 0.771185167 Simplifying x + -0.46875 = 0.771185167 Reorder the terms: -0.46875 + x = 0.771185167 Solving -0.46875 + x = 0.771185167 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 = 0.771185167 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = 0.771185167 + 0.46875 x = 0.771185167 + 0.46875 Combine like terms: 0.771185167 + 0.46875 = 1.239935167 x = 1.239935167 Simplifying x = 1.239935167Subproblem 2
x + -0.46875 = -0.771185167 Simplifying x + -0.46875 = -0.771185167 Reorder the terms: -0.46875 + x = -0.771185167 Solving -0.46875 + x = -0.771185167 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 = -0.771185167 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = -0.771185167 + 0.46875 x = -0.771185167 + 0.46875 Combine like terms: -0.771185167 + 0.46875 = -0.302435167 x = -0.302435167 Simplifying x = -0.302435167Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.239935167, -0.302435167}
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