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Simplifying (x + -2.3)(x + -2.3) = 25 Reorder the terms: (-2.3 + x)(x + -2.3) = 25 Reorder the terms: (-2.3 + x)(-2.3 + x) = 25 Multiply (-2.3 + x) * (-2.3 + x) (-2.3(-2.3 + x) + x(-2.3 + x)) = 25 ((-2.3 * -2.3 + x * -2.3) + x(-2.3 + x)) = 25 ((5.29 + -2.3x) + x(-2.3 + x)) = 25 (5.29 + -2.3x + (-2.3 * x + x * x)) = 25 (5.29 + -2.3x + (-2.3x + x2)) = 25 Combine like terms: -2.3x + -2.3x = -4.6x (5.29 + -4.6x + x2) = 25 Solving 5.29 + -4.6x + x2 = 25 Solving for variable 'x'. Reorder the terms: 5.29 + -25 + -4.6x + x2 = 25 + -25 Combine like terms: 5.29 + -25 = -19.71 -19.71 + -4.6x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -19.71 + -4.6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19.71' to each side of the equation. -19.71 + -4.6x + 19.71 + x2 = 0 + 19.71 Reorder the terms: -19.71 + 19.71 + -4.6x + x2 = 0 + 19.71 Combine like terms: -19.71 + 19.71 = 0.00 0.00 + -4.6x + x2 = 0 + 19.71 -4.6x + x2 = 0 + 19.71 Combine like terms: 0 + 19.71 = 19.71 -4.6x + x2 = 19.71 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = 19.71 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = 19.71 + 5.29 Combine like terms: 19.71 + 5.29 = 25 5.29 + -4.6x + x2 = 25 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + -2.3) equal to 5 and -5.Subproblem 1
x + -2.3 = 5 Simplifying x + -2.3 = 5 Reorder the terms: -2.3 + x = 5 Solving -2.3 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 5 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 5 + 2.3 x = 5 + 2.3 Combine like terms: 5 + 2.3 = 7.3 x = 7.3 Simplifying x = 7.3Subproblem 2
x + -2.3 = -5 Simplifying x + -2.3 = -5 Reorder the terms: -2.3 + x = -5 Solving -2.3 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -5 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -5 + 2.3 x = -5 + 2.3 Combine like terms: -5 + 2.3 = -2.7 x = -2.7 Simplifying x = -2.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.3, -2.7}
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