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Simplifying -1.5x2 + 18.75x + 16 = 0 Reorder the terms: 16 + 18.75x + -1.5x2 = 0 Solving 16 + 18.75x + -1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -10.66666667 + -12.5x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + -12.5x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + -12.5x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + -12.5x + x2 = 0 + 10.66666667 -12.5x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 -12.5x + x2 = 10.66666667 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 10.66666667 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 10.66666667 + 39.0625 Combine like terms: 10.66666667 + 39.0625 = 49.72916667 39.0625 + -12.5x + x2 = 49.72916667 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 49.72916667 Calculate the square root of the right side: 7.051891 Break this problem into two subproblems by setting (x + -6.25) equal to 7.051891 and -7.051891.Subproblem 1
x + -6.25 = 7.051891 Simplifying x + -6.25 = 7.051891 Reorder the terms: -6.25 + x = 7.051891 Solving -6.25 + x = 7.051891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 7.051891 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 7.051891 + 6.25 x = 7.051891 + 6.25 Combine like terms: 7.051891 + 6.25 = 13.301891 x = 13.301891 Simplifying x = 13.301891Subproblem 2
x + -6.25 = -7.051891 Simplifying x + -6.25 = -7.051891 Reorder the terms: -6.25 + x = -7.051891 Solving -6.25 + x = -7.051891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -7.051891 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -7.051891 + 6.25 x = -7.051891 + 6.25 Combine like terms: -7.051891 + 6.25 = -0.801891 x = -0.801891 Simplifying x = -0.801891Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.301891, -0.801891}
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