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Simplifying 0 = 2x2 + 4x + -10 Reorder the terms: 0 = -10 + 4x + 2x2 Solving 0 = -10 + 4x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + -4x + -2x2 = -10 + 4x + 2x2 + 10 + -4x + -2x2 Reorder the terms: 10 + -4x + -2x2 = -10 + 10 + 4x + -4x + 2x2 + -2x2 Combine like terms: -10 + 10 = 0 10 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2 10 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 10 + -4x + -2x2 = 0 + 2x2 + -2x2 10 + -4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 10 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -2x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + -2x + -1x2 = 0 Solving 5 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 2x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x + x2 = 0 + 5 2x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2x + x2 = 5 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 = 5 + 1 Reorder the terms: 1 + 2x + x2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2x + x2 = 6 Factor a perfect square on the left side: (x + 1)(x + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 1 = 2.449489743 Simplifying x + 1 = 2.449489743 Reorder the terms: 1 + x = 2.449489743 Solving 1 + x = 2.449489743 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 = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.449489743 + -1 x = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 x = 1.449489743 Simplifying x = 1.449489743Subproblem 2
x + 1 = -2.449489743 Simplifying x + 1 = -2.449489743 Reorder the terms: 1 + x = -2.449489743 Solving 1 + x = -2.449489743 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 = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.449489743 + -1 x = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 x = -3.449489743 Simplifying x = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.449489743, -3.449489743}Solution
x = {1.449489743, -3.449489743}
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