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Simplifying -5x(3 + -2x) = 4 (3 * -5x + -2x * -5x) = 4 (-15x + 10x2) = 4 Solving -15x + 10x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -15x + 10x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -15x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + -1.5x + x2 = 0.0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.5x + 0.4 + x2 = 0.0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.5x + x2 = 0.0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.5x + x2 = 0.0 + 0.4 -1.5x + x2 = 0.0 + 0.4 Combine like terms: 0.0 + 0.4 = 0.4 -1.5x + x2 = 0.4 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.4 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.4 + 0.5625 Combine like terms: 0.4 + 0.5625 = 0.9625 0.5625 + -1.5x + x2 = 0.9625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.9625 Calculate the square root of the right side: 0.981070844 Break this problem into two subproblems by setting (x + -0.75) equal to 0.981070844 and -0.981070844.Subproblem 1
x + -0.75 = 0.981070844 Simplifying x + -0.75 = 0.981070844 Reorder the terms: -0.75 + x = 0.981070844 Solving -0.75 + x = 0.981070844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.981070844 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.981070844 + 0.75 x = 0.981070844 + 0.75 Combine like terms: 0.981070844 + 0.75 = 1.731070844 x = 1.731070844 Simplifying x = 1.731070844Subproblem 2
x + -0.75 = -0.981070844 Simplifying x + -0.75 = -0.981070844 Reorder the terms: -0.75 + x = -0.981070844 Solving -0.75 + x = -0.981070844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.981070844 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.981070844 + 0.75 x = -0.981070844 + 0.75 Combine like terms: -0.981070844 + 0.75 = -0.231070844 x = -0.231070844 Simplifying x = -0.231070844Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.731070844, -0.231070844}
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