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Simplifying -0.04x2 + 7.5x + 10.2 = 0 Reorder the terms: 10.2 + 7.5x + -0.04x2 = 0 Solving 10.2 + 7.5x + -0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -255 + -187.5x + x2 = 0 Move the constant term to the right: Add '255' to each side of the equation. -255 + -187.5x + 255 + x2 = 0 + 255 Reorder the terms: -255 + 255 + -187.5x + x2 = 0 + 255 Combine like terms: -255 + 255 = 0 0 + -187.5x + x2 = 0 + 255 -187.5x + x2 = 0 + 255 Combine like terms: 0 + 255 = 255 -187.5x + x2 = 255 The x term is -187.5x. Take half its coefficient (-93.75). Square it (8789.0625) and add it to both sides. Add '8789.0625' to each side of the equation. -187.5x + 8789.0625 + x2 = 255 + 8789.0625 Reorder the terms: 8789.0625 + -187.5x + x2 = 255 + 8789.0625 Combine like terms: 255 + 8789.0625 = 9044.0625 8789.0625 + -187.5x + x2 = 9044.0625 Factor a perfect square on the left side: (x + -93.75)(x + -93.75) = 9044.0625 Calculate the square root of the right side: 95.100276025 Break this problem into two subproblems by setting (x + -93.75) equal to 95.100276025 and -95.100276025.Subproblem 1
x + -93.75 = 95.100276025 Simplifying x + -93.75 = 95.100276025 Reorder the terms: -93.75 + x = 95.100276025 Solving -93.75 + x = 95.100276025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '93.75' to each side of the equation. -93.75 + 93.75 + x = 95.100276025 + 93.75 Combine like terms: -93.75 + 93.75 = 0.00 0.00 + x = 95.100276025 + 93.75 x = 95.100276025 + 93.75 Combine like terms: 95.100276025 + 93.75 = 188.850276025 x = 188.850276025 Simplifying x = 188.850276025Subproblem 2
x + -93.75 = -95.100276025 Simplifying x + -93.75 = -95.100276025 Reorder the terms: -93.75 + x = -95.100276025 Solving -93.75 + x = -95.100276025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '93.75' to each side of the equation. -93.75 + 93.75 + x = -95.100276025 + 93.75 Combine like terms: -93.75 + 93.75 = 0.00 0.00 + x = -95.100276025 + 93.75 x = -95.100276025 + 93.75 Combine like terms: -95.100276025 + 93.75 = -1.350276025 x = -1.350276025 Simplifying x = -1.350276025Solution
The solution to the problem is based on the solutions from the subproblems. x = {188.850276025, -1.350276025}
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