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Simplifying 3x(x + -1.25) = 11.25 Reorder the terms: 3x(-1.25 + x) = 11.25 (-1.25 * 3x + x * 3x) = 11.25 (-3.75x + 3x2) = 11.25 Solving -3.75x + 3x2 = 11.25 Solving for variable 'x'. Reorder the terms: -11.25 + -3.75x + 3x2 = 11.25 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 -11.25 + -3.75x + 3x2 = 0.00 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.75 + -1.25x + x2 = 0.00 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -1.25x + 3.75 + x2 = 0.00 + 3.75 Reorder the terms: -3.75 + 3.75 + -1.25x + x2 = 0.00 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -1.25x + x2 = 0.00 + 3.75 -1.25x + x2 = 0.00 + 3.75 Combine like terms: 0.00 + 3.75 = 3.75 -1.25x + x2 = 3.75 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 3.75 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 3.75 + 0.390625 Combine like terms: 3.75 + 0.390625 = 4.140625 0.390625 + -1.25x + x2 = 4.140625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 4.140625 Calculate the square root of the right side: 2.034852575 Break this problem into two subproblems by setting (x + -0.625) equal to 2.034852575 and -2.034852575.Subproblem 1
x + -0.625 = 2.034852575 Simplifying x + -0.625 = 2.034852575 Reorder the terms: -0.625 + x = 2.034852575 Solving -0.625 + x = 2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 2.034852575 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 2.034852575 + 0.625 x = 2.034852575 + 0.625 Combine like terms: 2.034852575 + 0.625 = 2.659852575 x = 2.659852575 Simplifying x = 2.659852575Subproblem 2
x + -0.625 = -2.034852575 Simplifying x + -0.625 = -2.034852575 Reorder the terms: -0.625 + x = -2.034852575 Solving -0.625 + x = -2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -2.034852575 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -2.034852575 + 0.625 x = -2.034852575 + 0.625 Combine like terms: -2.034852575 + 0.625 = -1.409852575 x = -1.409852575 Simplifying x = -1.409852575Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.659852575, -1.409852575}
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