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Simplifying -10x2 + 38x + -25 = 0 Reorder the terms: -25 + 38x + -10x2 = 0 Solving -25 + 38x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 2.5 + -3.8x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -3.8x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -3.8x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -3.8x + x2 = 0 + -2.5 -3.8x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -3.8x + x2 = -2.5 The x term is -3.8x. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8x + 3.61 + x2 = -2.5 + 3.61 Reorder the terms: 3.61 + -3.8x + x2 = -2.5 + 3.61 Combine like terms: -2.5 + 3.61 = 1.11 3.61 + -3.8x + x2 = 1.11 Factor a perfect square on the left side: (x + -1.9)(x + -1.9) = 1.11 Calculate the square root of the right side: 1.053565375 Break this problem into two subproblems by setting (x + -1.9) equal to 1.053565375 and -1.053565375.Subproblem 1
x + -1.9 = 1.053565375 Simplifying x + -1.9 = 1.053565375 Reorder the terms: -1.9 + x = 1.053565375 Solving -1.9 + x = 1.053565375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = 1.053565375 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = 1.053565375 + 1.9 x = 1.053565375 + 1.9 Combine like terms: 1.053565375 + 1.9 = 2.953565375 x = 2.953565375 Simplifying x = 2.953565375Subproblem 2
x + -1.9 = -1.053565375 Simplifying x + -1.9 = -1.053565375 Reorder the terms: -1.9 + x = -1.053565375 Solving -1.9 + x = -1.053565375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = -1.053565375 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = -1.053565375 + 1.9 x = -1.053565375 + 1.9 Combine like terms: -1.053565375 + 1.9 = 0.846434625 x = 0.846434625 Simplifying x = 0.846434625Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.953565375, 0.846434625}
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