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Simplifying 5x(2x + -4) + -3(x + -2) = 4x + -2 Reorder the terms: 5x(-4 + 2x) + -3(x + -2) = 4x + -2 (-4 * 5x + 2x * 5x) + -3(x + -2) = 4x + -2 (-20x + 10x2) + -3(x + -2) = 4x + -2 Reorder the terms: -20x + 10x2 + -3(-2 + x) = 4x + -2 -20x + 10x2 + (-2 * -3 + x * -3) = 4x + -2 -20x + 10x2 + (6 + -3x) = 4x + -2 Reorder the terms: 6 + -20x + -3x + 10x2 = 4x + -2 Combine like terms: -20x + -3x = -23x 6 + -23x + 10x2 = 4x + -2 Reorder the terms: 6 + -23x + 10x2 = -2 + 4x Solving 6 + -23x + 10x2 = -2 + 4x Solving for variable 'x'. Reorder the terms: 6 + 2 + -23x + -4x + 10x2 = -2 + 4x + 2 + -4x Combine like terms: 6 + 2 = 8 8 + -23x + -4x + 10x2 = -2 + 4x + 2 + -4x Combine like terms: -23x + -4x = -27x 8 + -27x + 10x2 = -2 + 4x + 2 + -4x Reorder the terms: 8 + -27x + 10x2 = -2 + 2 + 4x + -4x Combine like terms: -2 + 2 = 0 8 + -27x + 10x2 = 0 + 4x + -4x 8 + -27x + 10x2 = 4x + -4x Combine like terms: 4x + -4x = 0 8 + -27x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.8 + -2.7x + x2 = 0.0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -2.7x + -0.8 + x2 = 0.0 + -0.8 Reorder the terms: 0.8 + -0.8 + -2.7x + x2 = 0.0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -2.7x + x2 = 0.0 + -0.8 -2.7x + x2 = 0.0 + -0.8 Combine like terms: 0.0 + -0.8 = -0.8 -2.7x + x2 = -0.8 The x term is -2.7x. Take half its coefficient (-1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. -2.7x + 1.8225 + x2 = -0.8 + 1.8225 Reorder the terms: 1.8225 + -2.7x + x2 = -0.8 + 1.8225 Combine like terms: -0.8 + 1.8225 = 1.0225 1.8225 + -2.7x + x2 = 1.0225 Factor a perfect square on the left side: (x + -1.35)(x + -1.35) = 1.0225 Calculate the square root of the right side: 1.011187421 Break this problem into two subproblems by setting (x + -1.35) equal to 1.011187421 and -1.011187421.Subproblem 1
x + -1.35 = 1.011187421 Simplifying x + -1.35 = 1.011187421 Reorder the terms: -1.35 + x = 1.011187421 Solving -1.35 + x = 1.011187421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = 1.011187421 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = 1.011187421 + 1.35 x = 1.011187421 + 1.35 Combine like terms: 1.011187421 + 1.35 = 2.361187421 x = 2.361187421 Simplifying x = 2.361187421Subproblem 2
x + -1.35 = -1.011187421 Simplifying x + -1.35 = -1.011187421 Reorder the terms: -1.35 + x = -1.011187421 Solving -1.35 + x = -1.011187421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = -1.011187421 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = -1.011187421 + 1.35 x = -1.011187421 + 1.35 Combine like terms: -1.011187421 + 1.35 = 0.338812579 x = 0.338812579 Simplifying x = 0.338812579Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.361187421, 0.338812579}
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