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Simplifying 4x(x + -3) + -5(3x + -6) = (2x + -3) * 2 Reorder the terms: 4x(-3 + x) + -5(3x + -6) = (2x + -3) * 2 (-3 * 4x + x * 4x) + -5(3x + -6) = (2x + -3) * 2 (-12x + 4x2) + -5(3x + -6) = (2x + -3) * 2 Reorder the terms: -12x + 4x2 + -5(-6 + 3x) = (2x + -3) * 2 -12x + 4x2 + (-6 * -5 + 3x * -5) = (2x + -3) * 2 -12x + 4x2 + (30 + -15x) = (2x + -3) * 2 Reorder the terms: 30 + -12x + -15x + 4x2 = (2x + -3) * 2 Combine like terms: -12x + -15x = -27x 30 + -27x + 4x2 = (2x + -3) * 2 Reorder the terms: 30 + -27x + 4x2 = (-3 + 2x) * 2 Reorder the terms for easier multiplication: 30 + -27x + 4x2 = 2(-3 + 2x) 30 + -27x + 4x2 = (-3 * 2 + 2x * 2) 30 + -27x + 4x2 = (-6 + 4x) Solving 30 + -27x + 4x2 = -6 + 4x Solving for variable 'x'. Reorder the terms: 30 + 6 + -27x + -4x + 4x2 = -6 + 4x + 6 + -4x Combine like terms: 30 + 6 = 36 36 + -27x + -4x + 4x2 = -6 + 4x + 6 + -4x Combine like terms: -27x + -4x = -31x 36 + -31x + 4x2 = -6 + 4x + 6 + -4x Reorder the terms: 36 + -31x + 4x2 = -6 + 6 + 4x + -4x Combine like terms: -6 + 6 = 0 36 + -31x + 4x2 = 0 + 4x + -4x 36 + -31x + 4x2 = 4x + -4x Combine like terms: 4x + -4x = 0 36 + -31x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9 + -7.75x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -7.75x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -7.75x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7.75x + x2 = 0 + -9 -7.75x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -7.75x + x2 = -9 The x term is -7.75x. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75x + 15.015625 + x2 = -9 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = -9 + 15.015625 Combine like terms: -9 + 15.015625 = 6.015625 15.015625 + -7.75x + x2 = 6.015625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (x + -3.875) equal to 2.452677109 and -2.452677109.Subproblem 1
x + -3.875 = 2.452677109 Simplifying x + -3.875 = 2.452677109 Reorder the terms: -3.875 + x = 2.452677109 Solving -3.875 + x = 2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = 2.452677109 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 2.452677109 + 3.875 x = 2.452677109 + 3.875 Combine like terms: 2.452677109 + 3.875 = 6.327677109 x = 6.327677109 Simplifying x = 6.327677109Subproblem 2
x + -3.875 = -2.452677109 Simplifying x + -3.875 = -2.452677109 Reorder the terms: -3.875 + x = -2.452677109 Solving -3.875 + x = -2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = -2.452677109 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -2.452677109 + 3.875 x = -2.452677109 + 3.875 Combine like terms: -2.452677109 + 3.875 = 1.422322891 x = 1.422322891 Simplifying x = 1.422322891Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.327677109, 1.422322891}
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