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Simplifying 5x2 + -10 = x * 2 + 90 Reorder the terms: -10 + 5x2 = x * 2 + 90 Reorder the terms for easier multiplication: -10 + 5x2 = 2x + 90 Reorder the terms: -10 + 5x2 = 90 + 2x Solving -10 + 5x2 = 90 + 2x Solving for variable 'x'. Reorder the terms: -10 + -90 + -2x + 5x2 = 90 + 2x + -90 + -2x Combine like terms: -10 + -90 = -100 -100 + -2x + 5x2 = 90 + 2x + -90 + -2x Reorder the terms: -100 + -2x + 5x2 = 90 + -90 + 2x + -2x Combine like terms: 90 + -90 = 0 -100 + -2x + 5x2 = 0 + 2x + -2x -100 + -2x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -100 + -2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -20 + -0.4x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -0.4x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -0.4x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -0.4x + x2 = 0 + 20 -0.4x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -0.4x + x2 = 20 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 20 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 20 + 0.04 Combine like terms: 20 + 0.04 = 20.04 0.04 + -0.4x + x2 = 20.04 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 20.04 Calculate the square root of the right side: 4.476605857 Break this problem into two subproblems by setting (x + -0.2) equal to 4.476605857 and -4.476605857.Subproblem 1
x + -0.2 = 4.476605857 Simplifying x + -0.2 = 4.476605857 Reorder the terms: -0.2 + x = 4.476605857 Solving -0.2 + x = 4.476605857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 4.476605857 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 4.476605857 + 0.2 x = 4.476605857 + 0.2 Combine like terms: 4.476605857 + 0.2 = 4.676605857 x = 4.676605857 Simplifying x = 4.676605857Subproblem 2
x + -0.2 = -4.476605857 Simplifying x + -0.2 = -4.476605857 Reorder the terms: -0.2 + x = -4.476605857 Solving -0.2 + x = -4.476605857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -4.476605857 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -4.476605857 + 0.2 x = -4.476605857 + 0.2 Combine like terms: -4.476605857 + 0.2 = -4.276605857 x = -4.276605857 Simplifying x = -4.276605857Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.676605857, -4.276605857}
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