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Simplifying -0.75x2 + 1.5x + 62.25 = 0 Reorder the terms: 62.25 + 1.5x + -0.75x2 = 0 Solving 62.25 + 1.5x + -0.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.75 the coefficient of the squared term: Divide each side by '-0.75'. -83 + -2x + x2 = 0 Move the constant term to the right: Add '83' to each side of the equation. -83 + -2x + 83 + x2 = 0 + 83 Reorder the terms: -83 + 83 + -2x + x2 = 0 + 83 Combine like terms: -83 + 83 = 0 0 + -2x + x2 = 0 + 83 -2x + x2 = 0 + 83 Combine like terms: 0 + 83 = 83 -2x + x2 = 83 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 83 + 1 Reorder the terms: 1 + -2x + x2 = 83 + 1 Combine like terms: 83 + 1 = 84 1 + -2x + x2 = 84 Factor a perfect square on the left side: (x + -1)(x + -1) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + -1) equal to 9.16515139 and -9.16515139.Subproblem 1
x + -1 = 9.16515139 Simplifying x + -1 = 9.16515139 Reorder the terms: -1 + x = 9.16515139 Solving -1 + x = 9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 9.16515139 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.16515139 + 1 x = 9.16515139 + 1 Combine like terms: 9.16515139 + 1 = 10.16515139 x = 10.16515139 Simplifying x = 10.16515139Subproblem 2
x + -1 = -9.16515139 Simplifying x + -1 = -9.16515139 Reorder the terms: -1 + x = -9.16515139 Solving -1 + x = -9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -9.16515139 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.16515139 + 1 x = -9.16515139 + 1 Combine like terms: -9.16515139 + 1 = -8.16515139 x = -8.16515139 Simplifying x = -8.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.16515139, -8.16515139}
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