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Simplifying 5(2x + -1) * 4x + 17 = 5x + 6(x + 2) Reorder the terms: 5(-1 + 2x) * 4x + 17 = 5x + 6(x + 2) Reorder the terms for easier multiplication: 5 * 4x(-1 + 2x) + 17 = 5x + 6(x + 2) Multiply 5 * 4 20x(-1 + 2x) + 17 = 5x + 6(x + 2) (-1 * 20x + 2x * 20x) + 17 = 5x + 6(x + 2) (-20x + 40x2) + 17 = 5x + 6(x + 2) Reorder the terms: 17 + -20x + 40x2 = 5x + 6(x + 2) Reorder the terms: 17 + -20x + 40x2 = 5x + 6(2 + x) 17 + -20x + 40x2 = 5x + (2 * 6 + x * 6) 17 + -20x + 40x2 = 5x + (12 + 6x) Reorder the terms: 17 + -20x + 40x2 = 12 + 5x + 6x Combine like terms: 5x + 6x = 11x 17 + -20x + 40x2 = 12 + 11x Solving 17 + -20x + 40x2 = 12 + 11x Solving for variable 'x'. Reorder the terms: 17 + -12 + -20x + -11x + 40x2 = 12 + 11x + -12 + -11x Combine like terms: 17 + -12 = 5 5 + -20x + -11x + 40x2 = 12 + 11x + -12 + -11x Combine like terms: -20x + -11x = -31x 5 + -31x + 40x2 = 12 + 11x + -12 + -11x Reorder the terms: 5 + -31x + 40x2 = 12 + -12 + 11x + -11x Combine like terms: 12 + -12 = 0 5 + -31x + 40x2 = 0 + 11x + -11x 5 + -31x + 40x2 = 11x + -11x Combine like terms: 11x + -11x = 0 5 + -31x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 0.125 + -0.775x + x2 = 0.0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -0.775x + -0.125 + x2 = 0.0 + -0.125 Reorder the terms: 0.125 + -0.125 + -0.775x + x2 = 0.0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -0.775x + x2 = 0.0 + -0.125 -0.775x + x2 = 0.0 + -0.125 Combine like terms: 0.0 + -0.125 = -0.125 -0.775x + x2 = -0.125 The x term is -0.775x. Take half its coefficient (-0.3875). Square it (0.15015625) and add it to both sides. Add '0.15015625' to each side of the equation. -0.775x + 0.15015625 + x2 = -0.125 + 0.15015625 Reorder the terms: 0.15015625 + -0.775x + x2 = -0.125 + 0.15015625 Combine like terms: -0.125 + 0.15015625 = 0.02515625 0.15015625 + -0.775x + x2 = 0.02515625 Factor a perfect square on the left side: (x + -0.3875)(x + -0.3875) = 0.02515625 Calculate the square root of the right side: 0.158607219 Break this problem into two subproblems by setting (x + -0.3875) equal to 0.158607219 and -0.158607219.Subproblem 1
x + -0.3875 = 0.158607219 Simplifying x + -0.3875 = 0.158607219 Reorder the terms: -0.3875 + x = 0.158607219 Solving -0.3875 + x = 0.158607219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3875' to each side of the equation. -0.3875 + 0.3875 + x = 0.158607219 + 0.3875 Combine like terms: -0.3875 + 0.3875 = 0.0000 0.0000 + x = 0.158607219 + 0.3875 x = 0.158607219 + 0.3875 Combine like terms: 0.158607219 + 0.3875 = 0.546107219 x = 0.546107219 Simplifying x = 0.546107219Subproblem 2
x + -0.3875 = -0.158607219 Simplifying x + -0.3875 = -0.158607219 Reorder the terms: -0.3875 + x = -0.158607219 Solving -0.3875 + x = -0.158607219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3875' to each side of the equation. -0.3875 + 0.3875 + x = -0.158607219 + 0.3875 Combine like terms: -0.3875 + 0.3875 = 0.0000 0.0000 + x = -0.158607219 + 0.3875 x = -0.158607219 + 0.3875 Combine like terms: -0.158607219 + 0.3875 = 0.228892781 x = 0.228892781 Simplifying x = 0.228892781Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.546107219, 0.228892781}
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