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Simplifying 3(x + -2) * 2 + 5x = x(3x + -4) + -40 Reorder the terms: 3(-2 + x) * 2 + 5x = x(3x + -4) + -40 Reorder the terms for easier multiplication: 3 * 2(-2 + x) + 5x = x(3x + -4) + -40 Multiply 3 * 2 6(-2 + x) + 5x = x(3x + -4) + -40 (-2 * 6 + x * 6) + 5x = x(3x + -4) + -40 (-12 + 6x) + 5x = x(3x + -4) + -40 Combine like terms: 6x + 5x = 11x -12 + 11x = x(3x + -4) + -40 Reorder the terms: -12 + 11x = x(-4 + 3x) + -40 -12 + 11x = (-4 * x + 3x * x) + -40 -12 + 11x = (-4x + 3x2) + -40 Reorder the terms: -12 + 11x = -40 + -4x + 3x2 Solving -12 + 11x = -40 + -4x + 3x2 Solving for variable 'x'. Reorder the terms: -12 + 40 + 11x + 4x + -3x2 = -40 + -4x + 3x2 + 40 + 4x + -3x2 Combine like terms: -12 + 40 = 28 28 + 11x + 4x + -3x2 = -40 + -4x + 3x2 + 40 + 4x + -3x2 Combine like terms: 11x + 4x = 15x 28 + 15x + -3x2 = -40 + -4x + 3x2 + 40 + 4x + -3x2 Reorder the terms: 28 + 15x + -3x2 = -40 + 40 + -4x + 4x + 3x2 + -3x2 Combine like terms: -40 + 40 = 0 28 + 15x + -3x2 = 0 + -4x + 4x + 3x2 + -3x2 28 + 15x + -3x2 = -4x + 4x + 3x2 + -3x2 Combine like terms: -4x + 4x = 0 28 + 15x + -3x2 = 0 + 3x2 + -3x2 28 + 15x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 28 + 15x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -9.333333333 + -5x + x2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -5x + 9.333333333 + x2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -5x + x2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -5x + x2 = 0 + 9.333333333 -5x + x2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -5x + x2 = 9.333333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 9.333333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 9.333333333 + 6.25 Combine like terms: 9.333333333 + 6.25 = 15.583333333 6.25 + -5x + x2 = 15.583333333 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 15.583333333 Calculate the square root of the right side: 3.947573094 Break this problem into two subproblems by setting (x + -2.5) equal to 3.947573094 and -3.947573094.Subproblem 1
x + -2.5 = 3.947573094 Simplifying x + -2.5 = 3.947573094 Reorder the terms: -2.5 + x = 3.947573094 Solving -2.5 + x = 3.947573094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.947573094 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.947573094 + 2.5 x = 3.947573094 + 2.5 Combine like terms: 3.947573094 + 2.5 = 6.447573094 x = 6.447573094 Simplifying x = 6.447573094Subproblem 2
x + -2.5 = -3.947573094 Simplifying x + -2.5 = -3.947573094 Reorder the terms: -2.5 + x = -3.947573094 Solving -2.5 + x = -3.947573094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.947573094 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.947573094 + 2.5 x = -3.947573094 + 2.5 Combine like terms: -3.947573094 + 2.5 = -1.447573094 x = -1.447573094 Simplifying x = -1.447573094Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.447573094, -1.447573094}
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