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Simplifying 5x(-2 + -1x) + 7 = 2 (-2 * 5x + -1x * 5x) + 7 = 2 (-10x + -5x2) + 7 = 2 Reorder the terms: 7 + -10x + -5x2 = 2 Solving 7 + -10x + -5x2 = 2 Solving for variable 'x'. Reorder the terms: 7 + -2 + -10x + -5x2 = 2 + -2 Combine like terms: 7 + -2 = 5 5 + -10x + -5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 5 + -10x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -2x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -2x + -1x2)' equal to zero and attempt to solve: Simplifying 1 + -2x + -1x2 = 0 Solving 1 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 2x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 2x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 2x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x + x2 = 0 + 1 2x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 2x + x2 = 1 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1 + 1 Reorder the terms: 1 + 2x + x2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2x + x2 = 2 Factor a perfect square on the left side: (x + 1)(x + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 1) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 1 = 1.414213562 Simplifying x + 1 = 1.414213562 Reorder the terms: 1 + x = 1.414213562 Solving 1 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.414213562 + -1 x = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 x = 0.414213562 Simplifying x = 0.414213562Subproblem 2
x + 1 = -1.414213562 Simplifying x + 1 = -1.414213562 Reorder the terms: 1 + x = -1.414213562 Solving 1 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.414213562 + -1 x = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 x = -2.414213562 Simplifying x = -2.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.414213562, -2.414213562}Solution
x = {0.414213562, -2.414213562}
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