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Simplifying 4x2 + 10x = 27 Reorder the terms: 10x + 4x2 = 27 Solving 10x + 4x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 10x + 4x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + 2.5x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + 2.5x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + 2.5x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + 2.5x + x2 = 0 + 6.75 2.5x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 2.5x + x2 = 6.75 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 = 6.75 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 6.75 + 1.5625 Combine like terms: 6.75 + 1.5625 = 8.3125 1.5625 + 2.5x + x2 = 8.3125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 8.3125 Calculate the square root of the right side: 2.883140649 Break this problem into two subproblems by setting (x + 1.25) equal to 2.883140649 and -2.883140649.Subproblem 1
x + 1.25 = 2.883140649 Simplifying x + 1.25 = 2.883140649 Reorder the terms: 1.25 + x = 2.883140649 Solving 1.25 + x = 2.883140649 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 = 2.883140649 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.883140649 + -1.25 x = 2.883140649 + -1.25 Combine like terms: 2.883140649 + -1.25 = 1.633140649 x = 1.633140649 Simplifying x = 1.633140649Subproblem 2
x + 1.25 = -2.883140649 Simplifying x + 1.25 = -2.883140649 Reorder the terms: 1.25 + x = -2.883140649 Solving 1.25 + x = -2.883140649 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 = -2.883140649 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.883140649 + -1.25 x = -2.883140649 + -1.25 Combine like terms: -2.883140649 + -1.25 = -4.133140649 x = -4.133140649 Simplifying x = -4.133140649Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.633140649, -4.133140649}
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