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Simplifying 5x(2x + 3) + -1(2x + -1) = 0 Reorder the terms: 5x(3 + 2x) + -1(2x + -1) = 0 (3 * 5x + 2x * 5x) + -1(2x + -1) = 0 (15x + 10x2) + -1(2x + -1) = 0 Reorder the terms: 15x + 10x2 + -1(-1 + 2x) = 0 15x + 10x2 + (-1 * -1 + 2x * -1) = 0 15x + 10x2 + (1 + -2x) = 0 Reorder the terms: 1 + 15x + -2x + 10x2 = 0 Combine like terms: 15x + -2x = 13x 1 + 13x + 10x2 = 0 Solving 1 + 13x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.1 + 1.3x + x2 = 0.0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 1.3x + -0.1 + x2 = 0.0 + -0.1 Reorder the terms: 0.1 + -0.1 + 1.3x + x2 = 0.0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 1.3x + x2 = 0.0 + -0.1 1.3x + x2 = 0.0 + -0.1 Combine like terms: 0.0 + -0.1 = -0.1 1.3x + x2 = -0.1 The x term is 1.3x. Take half its coefficient (0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. 1.3x + 0.4225 + x2 = -0.1 + 0.4225 Reorder the terms: 0.4225 + 1.3x + x2 = -0.1 + 0.4225 Combine like terms: -0.1 + 0.4225 = 0.3225 0.4225 + 1.3x + x2 = 0.3225 Factor a perfect square on the left side: (x + 0.65)(x + 0.65) = 0.3225 Calculate the square root of the right side: 0.567890835 Break this problem into two subproblems by setting (x + 0.65) equal to 0.567890835 and -0.567890835.Subproblem 1
x + 0.65 = 0.567890835 Simplifying x + 0.65 = 0.567890835 Reorder the terms: 0.65 + x = 0.567890835 Solving 0.65 + x = 0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = 0.567890835 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = 0.567890835 + -0.65 x = 0.567890835 + -0.65 Combine like terms: 0.567890835 + -0.65 = -0.082109165 x = -0.082109165 Simplifying x = -0.082109165Subproblem 2
x + 0.65 = -0.567890835 Simplifying x + 0.65 = -0.567890835 Reorder the terms: 0.65 + x = -0.567890835 Solving 0.65 + x = -0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = -0.567890835 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = -0.567890835 + -0.65 x = -0.567890835 + -0.65 Combine like terms: -0.567890835 + -0.65 = -1.217890835 x = -1.217890835 Simplifying x = -1.217890835Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.082109165, -1.217890835}
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