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Simplifying 2x + 5(1 + -1x2(2)) = 0 Reorder the terms for easier multiplication: 2x + 5(1 + -1 * 2x2) = 0 Multiply -1 * 2 2x + 5(1 + -2x2) = 0 2x + (1 * 5 + -2x2 * 5) = 0 2x + (5 + -10x2) = 0 Reorder the terms: 5 + 2x + -10x2 = 0 Solving 5 + 2x + -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'. -0.5 + -0.2x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.2x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.2x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.2x + x2 = 0.0 + 0.5 -0.2x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 -0.2x + x2 = 0.5 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 0.5 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 0.5 + 0.01 Combine like terms: 0.5 + 0.01 = 0.51 0.01 + -0.2x + x2 = 0.51 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.51 Calculate the square root of the right side: 0.714142843 Break this problem into two subproblems by setting (x + -0.1) equal to 0.714142843 and -0.714142843.Subproblem 1
x + -0.1 = 0.714142843 Simplifying x + -0.1 = 0.714142843 Reorder the terms: -0.1 + x = 0.714142843 Solving -0.1 + x = 0.714142843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0.714142843 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.714142843 + 0.1 x = 0.714142843 + 0.1 Combine like terms: 0.714142843 + 0.1 = 0.814142843 x = 0.814142843 Simplifying x = 0.814142843Subproblem 2
x + -0.1 = -0.714142843 Simplifying x + -0.1 = -0.714142843 Reorder the terms: -0.1 + x = -0.714142843 Solving -0.1 + x = -0.714142843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -0.714142843 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.714142843 + 0.1 x = -0.714142843 + 0.1 Combine like terms: -0.714142843 + 0.1 = -0.614142843 x = -0.614142843 Simplifying x = -0.614142843Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.814142843, -0.614142843}
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