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Simplifying 5x(3x + 1) = x + -2(x + -4) Reorder the terms: 5x(1 + 3x) = x + -2(x + -4) (1 * 5x + 3x * 5x) = x + -2(x + -4) (5x + 15x2) = x + -2(x + -4) Reorder the terms: 5x + 15x2 = x + -2(-4 + x) 5x + 15x2 = x + (-4 * -2 + x * -2) 5x + 15x2 = x + (8 + -2x) Reorder the terms: 5x + 15x2 = 8 + x + -2x Combine like terms: x + -2x = -1x 5x + 15x2 = 8 + -1x Solving 5x + 15x2 = 8 + -1x Solving for variable 'x'. Reorder the terms: -8 + 5x + x + 15x2 = 8 + -1x + -8 + x Combine like terms: 5x + x = 6x -8 + 6x + 15x2 = 8 + -1x + -8 + x Reorder the terms: -8 + 6x + 15x2 = 8 + -8 + -1x + x Combine like terms: 8 + -8 = 0 -8 + 6x + 15x2 = 0 + -1x + x -8 + 6x + 15x2 = -1x + x Combine like terms: -1x + x = 0 -8 + 6x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.5333333333 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.5333333333' to each side of the equation. -0.5333333333 + 0.4x + 0.5333333333 + x2 = 0 + 0.5333333333 Reorder the terms: -0.5333333333 + 0.5333333333 + 0.4x + x2 = 0 + 0.5333333333 Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000 0.0000000000 + 0.4x + x2 = 0 + 0.5333333333 0.4x + x2 = 0 + 0.5333333333 Combine like terms: 0 + 0.5333333333 = 0.5333333333 0.4x + x2 = 0.5333333333 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.5333333333 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.5333333333 + 0.04 Combine like terms: 0.5333333333 + 0.04 = 0.5733333333 0.04 + 0.4x + x2 = 0.5733333333 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.5733333333 Calculate the square root of the right side: 0.757187779 Break this problem into two subproblems by setting (x + 0.2) equal to 0.757187779 and -0.757187779.Subproblem 1
x + 0.2 = 0.757187779 Simplifying x + 0.2 = 0.757187779 Reorder the terms: 0.2 + x = 0.757187779 Solving 0.2 + x = 0.757187779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.757187779 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.757187779 + -0.2 x = 0.757187779 + -0.2 Combine like terms: 0.757187779 + -0.2 = 0.557187779 x = 0.557187779 Simplifying x = 0.557187779Subproblem 2
x + 0.2 = -0.757187779 Simplifying x + 0.2 = -0.757187779 Reorder the terms: 0.2 + x = -0.757187779 Solving 0.2 + x = -0.757187779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.757187779 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.757187779 + -0.2 x = -0.757187779 + -0.2 Combine like terms: -0.757187779 + -0.2 = -0.957187779 x = -0.957187779 Simplifying x = -0.957187779Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.557187779, -0.957187779}
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