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Simplifying 0.10x + 0.25x(24 + -1x) = 4.50 0.10x + (24 * 0.25x + -1x * 0.25x) = 4.50 0.10x + (6x + -0.25x2) = 4.50 Combine like terms: 0.10x + 6x = 6.1x 6.1x + -0.25x2 = 4.50 Solving 6.1x + -0.25x2 = 4.50 Solving for variable 'x'. Reorder the terms: -4.50 + 6.1x + -0.25x2 = 4.50 + -4.50 Combine like terms: 4.50 + -4.50 = 0.00 -4.50 + 6.1x + -0.25x2 = 0.00 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. 18 + -24.4x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -24.4x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -24.4x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -24.4x + x2 = 0 + -18 -24.4x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -24.4x + x2 = -18 The x term is -24.4x. Take half its coefficient (-12.2). Square it (148.84) and add it to both sides. Add '148.84' to each side of the equation. -24.4x + 148.84 + x2 = -18 + 148.84 Reorder the terms: 148.84 + -24.4x + x2 = -18 + 148.84 Combine like terms: -18 + 148.84 = 130.84 148.84 + -24.4x + x2 = 130.84 Factor a perfect square on the left side: (x + -12.2)(x + -12.2) = 130.84 Calculate the square root of the right side: 11.438531374 Break this problem into two subproblems by setting (x + -12.2) equal to 11.438531374 and -11.438531374.Subproblem 1
x + -12.2 = 11.438531374 Simplifying x + -12.2 = 11.438531374 Reorder the terms: -12.2 + x = 11.438531374 Solving -12.2 + x = 11.438531374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.2' to each side of the equation. -12.2 + 12.2 + x = 11.438531374 + 12.2 Combine like terms: -12.2 + 12.2 = 0.0 0.0 + x = 11.438531374 + 12.2 x = 11.438531374 + 12.2 Combine like terms: 11.438531374 + 12.2 = 23.638531374 x = 23.638531374 Simplifying x = 23.638531374Subproblem 2
x + -12.2 = -11.438531374 Simplifying x + -12.2 = -11.438531374 Reorder the terms: -12.2 + x = -11.438531374 Solving -12.2 + x = -11.438531374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.2' to each side of the equation. -12.2 + 12.2 + x = -11.438531374 + 12.2 Combine like terms: -12.2 + 12.2 = 0.0 0.0 + x = -11.438531374 + 12.2 x = -11.438531374 + 12.2 Combine like terms: -11.438531374 + 12.2 = 0.761468626 x = 0.761468626 Simplifying x = 0.761468626Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.638531374, 0.761468626}
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