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Simplifying 0 = -16x2 + 15x + 75 Reorder the terms: 0 = 75 + 15x + -16x2 Solving 0 = 75 + 15x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -75 = -75 -75 + -15x + 16x2 = 75 + 15x + -16x2 + -75 + -15x + 16x2 Reorder the terms: -75 + -15x + 16x2 = 75 + -75 + 15x + -15x + -16x2 + 16x2 Combine like terms: 75 + -75 = 0 -75 + -15x + 16x2 = 0 + 15x + -15x + -16x2 + 16x2 -75 + -15x + 16x2 = 15x + -15x + -16x2 + 16x2 Combine like terms: 15x + -15x = 0 -75 + -15x + 16x2 = 0 + -16x2 + 16x2 -75 + -15x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -75 + -15x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -4.6875 + -0.9375x + x2 = 0 Move the constant term to the right: Add '4.6875' to each side of the equation. -4.6875 + -0.9375x + 4.6875 + x2 = 0 + 4.6875 Reorder the terms: -4.6875 + 4.6875 + -0.9375x + x2 = 0 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + -0.9375x + x2 = 0 + 4.6875 -0.9375x + x2 = 0 + 4.6875 Combine like terms: 0 + 4.6875 = 4.6875 -0.9375x + x2 = 4.6875 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 = 4.6875 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375x + x2 = 4.6875 + 0.2197265625 Combine like terms: 4.6875 + 0.2197265625 = 4.9072265625 0.2197265625 + -0.9375x + x2 = 4.9072265625 Factor a perfect square on the left side: (x + -0.46875)(x + -0.46875) = 4.9072265625 Calculate the square root of the right side: 2.215226075 Break this problem into two subproblems by setting (x + -0.46875) equal to 2.215226075 and -2.215226075.Subproblem 1
x + -0.46875 = 2.215226075 Simplifying x + -0.46875 = 2.215226075 Reorder the terms: -0.46875 + x = 2.215226075 Solving -0.46875 + x = 2.215226075 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 = 2.215226075 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = 2.215226075 + 0.46875 x = 2.215226075 + 0.46875 Combine like terms: 2.215226075 + 0.46875 = 2.683976075 x = 2.683976075 Simplifying x = 2.683976075Subproblem 2
x + -0.46875 = -2.215226075 Simplifying x + -0.46875 = -2.215226075 Reorder the terms: -0.46875 + x = -2.215226075 Solving -0.46875 + x = -2.215226075 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 = -2.215226075 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = -2.215226075 + 0.46875 x = -2.215226075 + 0.46875 Combine like terms: -2.215226075 + 0.46875 = -1.746476075 x = -1.746476075 Simplifying x = -1.746476075Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.683976075, -1.746476075}
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