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Simplifying 5x2 + -2x + -26 = 0 Reorder the terms: -26 + -2x + 5x2 = 0 Solving -26 + -2x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.2 + -0.4x + x2 = 0 Move the constant term to the right: Add '5.2' to each side of the equation. -5.2 + -0.4x + 5.2 + x2 = 0 + 5.2 Reorder the terms: -5.2 + 5.2 + -0.4x + x2 = 0 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + -0.4x + x2 = 0 + 5.2 -0.4x + x2 = 0 + 5.2 Combine like terms: 0 + 5.2 = 5.2 -0.4x + x2 = 5.2 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 5.2 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 5.2 + 0.04 Combine like terms: 5.2 + 0.04 = 5.24 0.04 + -0.4x + x2 = 5.24 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 5.24 Calculate the square root of the right side: 2.289104628 Break this problem into two subproblems by setting (x + -0.2) equal to 2.289104628 and -2.289104628.Subproblem 1
x + -0.2 = 2.289104628 Simplifying x + -0.2 = 2.289104628 Reorder the terms: -0.2 + x = 2.289104628 Solving -0.2 + x = 2.289104628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 2.289104628 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 2.289104628 + 0.2 x = 2.289104628 + 0.2 Combine like terms: 2.289104628 + 0.2 = 2.489104628 x = 2.489104628 Simplifying x = 2.489104628Subproblem 2
x + -0.2 = -2.289104628 Simplifying x + -0.2 = -2.289104628 Reorder the terms: -0.2 + x = -2.289104628 Solving -0.2 + x = -2.289104628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -2.289104628 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -2.289104628 + 0.2 x = -2.289104628 + 0.2 Combine like terms: -2.289104628 + 0.2 = -2.089104628 x = -2.089104628 Simplifying x = -2.089104628Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.489104628, -2.089104628}
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