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Simplifying 10x2 + -247x + 400 = 0 Reorder the terms: 400 + -247x + 10x2 = 0 Solving 400 + -247x + 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'. 40 + -24.7x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -24.7x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -24.7x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -24.7x + x2 = 0 + -40 -24.7x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -24.7x + x2 = -40 The x term is -24.7x. Take half its coefficient (-12.35). Square it (152.5225) and add it to both sides. Add '152.5225' to each side of the equation. -24.7x + 152.5225 + x2 = -40 + 152.5225 Reorder the terms: 152.5225 + -24.7x + x2 = -40 + 152.5225 Combine like terms: -40 + 152.5225 = 112.5225 152.5225 + -24.7x + x2 = 112.5225 Factor a perfect square on the left side: (x + -12.35)(x + -12.35) = 112.5225 Calculate the square root of the right side: 10.607662325 Break this problem into two subproblems by setting (x + -12.35) equal to 10.607662325 and -10.607662325.Subproblem 1
x + -12.35 = 10.607662325 Simplifying x + -12.35 = 10.607662325 Reorder the terms: -12.35 + x = 10.607662325 Solving -12.35 + x = 10.607662325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.35' to each side of the equation. -12.35 + 12.35 + x = 10.607662325 + 12.35 Combine like terms: -12.35 + 12.35 = 0.00 0.00 + x = 10.607662325 + 12.35 x = 10.607662325 + 12.35 Combine like terms: 10.607662325 + 12.35 = 22.957662325 x = 22.957662325 Simplifying x = 22.957662325Subproblem 2
x + -12.35 = -10.607662325 Simplifying x + -12.35 = -10.607662325 Reorder the terms: -12.35 + x = -10.607662325 Solving -12.35 + x = -10.607662325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.35' to each side of the equation. -12.35 + 12.35 + x = -10.607662325 + 12.35 Combine like terms: -12.35 + 12.35 = 0.00 0.00 + x = -10.607662325 + 12.35 x = -10.607662325 + 12.35 Combine like terms: -10.607662325 + 12.35 = 1.742337675 x = 1.742337675 Simplifying x = 1.742337675Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.957662325, 1.742337675}
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