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Simplifying 4x2 + 10x + 4 = 207 Reorder the terms: 4 + 10x + 4x2 = 207 Solving 4 + 10x + 4x2 = 207 Solving for variable 'x'. Reorder the terms: 4 + -207 + 10x + 4x2 = 207 + -207 Combine like terms: 4 + -207 = -203 -203 + 10x + 4x2 = 207 + -207 Combine like terms: 207 + -207 = 0 -203 + 10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -50.75 + 2.5x + x2 = 0 Move the constant term to the right: Add '50.75' to each side of the equation. -50.75 + 2.5x + 50.75 + x2 = 0 + 50.75 Reorder the terms: -50.75 + 50.75 + 2.5x + x2 = 0 + 50.75 Combine like terms: -50.75 + 50.75 = 0.00 0.00 + 2.5x + x2 = 0 + 50.75 2.5x + x2 = 0 + 50.75 Combine like terms: 0 + 50.75 = 50.75 2.5x + x2 = 50.75 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 = 50.75 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 50.75 + 1.5625 Combine like terms: 50.75 + 1.5625 = 52.3125 1.5625 + 2.5x + x2 = 52.3125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 52.3125 Calculate the square root of the right side: 7.232738071 Break this problem into two subproblems by setting (x + 1.25) equal to 7.232738071 and -7.232738071.Subproblem 1
x + 1.25 = 7.232738071 Simplifying x + 1.25 = 7.232738071 Reorder the terms: 1.25 + x = 7.232738071 Solving 1.25 + x = 7.232738071 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 = 7.232738071 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 7.232738071 + -1.25 x = 7.232738071 + -1.25 Combine like terms: 7.232738071 + -1.25 = 5.982738071 x = 5.982738071 Simplifying x = 5.982738071Subproblem 2
x + 1.25 = -7.232738071 Simplifying x + 1.25 = -7.232738071 Reorder the terms: 1.25 + x = -7.232738071 Solving 1.25 + x = -7.232738071 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 = -7.232738071 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -7.232738071 + -1.25 x = -7.232738071 + -1.25 Combine like terms: -7.232738071 + -1.25 = -8.482738071 x = -8.482738071 Simplifying x = -8.482738071Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.982738071, -8.482738071}
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