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Simplifying -16x2 + 15x + 300 = 0 Reorder the terms: 300 + 15x + -16x2 = 0 Solving 300 + 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'. -18.75 + -0.9375x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + -0.9375x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + -0.9375x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + -0.9375x + x2 = 0 + 18.75 -0.9375x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 -0.9375x + x2 = 18.75 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 = 18.75 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375x + x2 = 18.75 + 0.2197265625 Combine like terms: 18.75 + 0.2197265625 = 18.9697265625 0.2197265625 + -0.9375x + x2 = 18.9697265625 Factor a perfect square on the left side: (x + -0.46875)(x + -0.46875) = 18.9697265625 Calculate the square root of the right side: 4.355424958 Break this problem into two subproblems by setting (x + -0.46875) equal to 4.355424958 and -4.355424958.Subproblem 1
x + -0.46875 = 4.355424958 Simplifying x + -0.46875 = 4.355424958 Reorder the terms: -0.46875 + x = 4.355424958 Solving -0.46875 + x = 4.355424958 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 = 4.355424958 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = 4.355424958 + 0.46875 x = 4.355424958 + 0.46875 Combine like terms: 4.355424958 + 0.46875 = 4.824174958 x = 4.824174958 Simplifying x = 4.824174958Subproblem 2
x + -0.46875 = -4.355424958 Simplifying x + -0.46875 = -4.355424958 Reorder the terms: -0.46875 + x = -4.355424958 Solving -0.46875 + x = -4.355424958 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 = -4.355424958 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = -4.355424958 + 0.46875 x = -4.355424958 + 0.46875 Combine like terms: -4.355424958 + 0.46875 = -3.886674958 x = -3.886674958 Simplifying x = -3.886674958Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.824174958, -3.886674958}
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