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Simplifying 2x(4 + 5x) = 5 + 10 (4 * 2x + 5x * 2x) = 5 + 10 (8x + 10x2) = 5 + 10 Combine like terms: 5 + 10 = 15 8x + 10x2 = 15 Solving 8x + 10x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 8x + 10x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 8x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.5 + 0.8x + x2 = 0.0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.8x + 1.5 + x2 = 0.0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.8x + x2 = 0.0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.8x + x2 = 0.0 + 1.5 0.8x + x2 = 0.0 + 1.5 Combine like terms: 0.0 + 1.5 = 1.5 0.8x + x2 = 1.5 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 1.5 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 1.5 + 0.16 Combine like terms: 1.5 + 0.16 = 1.66 0.16 + 0.8x + x2 = 1.66 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 1.66 Calculate the square root of the right side: 1.288409873 Break this problem into two subproblems by setting (x + 0.4) equal to 1.288409873 and -1.288409873.Subproblem 1
x + 0.4 = 1.288409873 Simplifying x + 0.4 = 1.288409873 Reorder the terms: 0.4 + x = 1.288409873 Solving 0.4 + x = 1.288409873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.288409873 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.288409873 + -0.4 x = 1.288409873 + -0.4 Combine like terms: 1.288409873 + -0.4 = 0.888409873 x = 0.888409873 Simplifying x = 0.888409873Subproblem 2
x + 0.4 = -1.288409873 Simplifying x + 0.4 = -1.288409873 Reorder the terms: 0.4 + x = -1.288409873 Solving 0.4 + x = -1.288409873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.288409873 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.288409873 + -0.4 x = -1.288409873 + -0.4 Combine like terms: -1.288409873 + -0.4 = -1.688409873 x = -1.688409873 Simplifying x = -1.688409873Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.888409873, -1.688409873}
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