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Simplifying 2x * 2x + 10x = 299 Reorder the terms for easier multiplication: 2 * 2x * x + 10x = 299 Multiply 2 * 2 4x * x + 10x = 299 Multiply x * x 4x2 + 10x = 299 Reorder the terms: 10x + 4x2 = 299 Solving 10x + 4x2 = 299 Solving for variable 'x'. Reorder the terms: -299 + 10x + 4x2 = 299 + -299 Combine like terms: 299 + -299 = 0 -299 + 10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -74.75 + 2.5x + x2 = 0 Move the constant term to the right: Add '74.75' to each side of the equation. -74.75 + 2.5x + 74.75 + x2 = 0 + 74.75 Reorder the terms: -74.75 + 74.75 + 2.5x + x2 = 0 + 74.75 Combine like terms: -74.75 + 74.75 = 0.00 0.00 + 2.5x + x2 = 0 + 74.75 2.5x + x2 = 0 + 74.75 Combine like terms: 0 + 74.75 = 74.75 2.5x + x2 = 74.75 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 74.75 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 74.75 + 1.5625 Combine like terms: 74.75 + 1.5625 = 76.3125 1.5625 + 2.5x + x2 = 76.3125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 76.3125 Calculate the square root of the right side: 8.735702605 Break this problem into two subproblems by setting (x + 1.25) equal to 8.735702605 and -8.735702605.Subproblem 1
x + 1.25 = 8.735702605 Simplifying x + 1.25 = 8.735702605 Reorder the terms: 1.25 + x = 8.735702605 Solving 1.25 + x = 8.735702605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 8.735702605 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 8.735702605 + -1.25 x = 8.735702605 + -1.25 Combine like terms: 8.735702605 + -1.25 = 7.485702605 x = 7.485702605 Simplifying x = 7.485702605Subproblem 2
x + 1.25 = -8.735702605 Simplifying x + 1.25 = -8.735702605 Reorder the terms: 1.25 + x = -8.735702605 Solving 1.25 + x = -8.735702605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -8.735702605 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -8.735702605 + -1.25 x = -8.735702605 + -1.25 Combine like terms: -8.735702605 + -1.25 = -9.985702605 x = -9.985702605 Simplifying x = -9.985702605Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.485702605, -9.985702605}
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