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Simplifying 4(2x + -5) * 3x = 21x + -6x + -20 Reorder the terms: 4(-5 + 2x) * 3x = 21x + -6x + -20 Reorder the terms for easier multiplication: 4 * 3x(-5 + 2x) = 21x + -6x + -20 Multiply 4 * 3 12x(-5 + 2x) = 21x + -6x + -20 (-5 * 12x + 2x * 12x) = 21x + -6x + -20 (-60x + 24x2) = 21x + -6x + -20 Reorder the terms: -60x + 24x2 = -20 + 21x + -6x Combine like terms: 21x + -6x = 15x -60x + 24x2 = -20 + 15x Solving -60x + 24x2 = -20 + 15x Solving for variable 'x'. Reorder the terms: 20 + -60x + -15x + 24x2 = -20 + 15x + 20 + -15x Combine like terms: -60x + -15x = -75x 20 + -75x + 24x2 = -20 + 15x + 20 + -15x Reorder the terms: 20 + -75x + 24x2 = -20 + 20 + 15x + -15x Combine like terms: -20 + 20 = 0 20 + -75x + 24x2 = 0 + 15x + -15x 20 + -75x + 24x2 = 15x + -15x Combine like terms: 15x + -15x = 0 20 + -75x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.8333333333 + -3.125x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -3.125x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -3.125x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -3.125x + x2 = 0 + -0.8333333333 -3.125x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -3.125x + x2 = -0.8333333333 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = -0.8333333333 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = -0.8333333333 + 2.44140625 Combine like terms: -0.8333333333 + 2.44140625 = 1.6080729167 2.44140625 + -3.125x + x2 = 1.6080729167 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 1.6080729167 Calculate the square root of the right side: 1.268098149 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.268098149 and -1.268098149.Subproblem 1
x + -1.5625 = 1.268098149 Simplifying x + -1.5625 = 1.268098149 Reorder the terms: -1.5625 + x = 1.268098149 Solving -1.5625 + x = 1.268098149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.268098149 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.268098149 + 1.5625 x = 1.268098149 + 1.5625 Combine like terms: 1.268098149 + 1.5625 = 2.830598149 x = 2.830598149 Simplifying x = 2.830598149Subproblem 2
x + -1.5625 = -1.268098149 Simplifying x + -1.5625 = -1.268098149 Reorder the terms: -1.5625 + x = -1.268098149 Solving -1.5625 + x = -1.268098149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.268098149 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.268098149 + 1.5625 x = -1.268098149 + 1.5625 Combine like terms: -1.268098149 + 1.5625 = 0.294401851 x = 0.294401851 Simplifying x = 0.294401851Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.830598149, 0.294401851}
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