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Simplifying 5x2 + 10x + -27 = 0 Reorder the terms: -27 + 10x + 5x2 = 0 Solving -27 + 10x + 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'. -5.4 + 2x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 2x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 2x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 2x + x2 = 0 + 5.4 2x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 2x + x2 = 5.4 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 = 5.4 + 1 Reorder the terms: 1 + 2x + x2 = 5.4 + 1 Combine like terms: 5.4 + 1 = 6.4 1 + 2x + x2 = 6.4 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.4 Calculate the square root of the right side: 2.529822128 Break this problem into two subproblems by setting (x + 1) equal to 2.529822128 and -2.529822128.Subproblem 1
x + 1 = 2.529822128 Simplifying x + 1 = 2.529822128 Reorder the terms: 1 + x = 2.529822128 Solving 1 + x = 2.529822128 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 = 2.529822128 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.529822128 + -1 x = 2.529822128 + -1 Combine like terms: 2.529822128 + -1 = 1.529822128 x = 1.529822128 Simplifying x = 1.529822128Subproblem 2
x + 1 = -2.529822128 Simplifying x + 1 = -2.529822128 Reorder the terms: 1 + x = -2.529822128 Solving 1 + x = -2.529822128 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 = -2.529822128 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.529822128 + -1 x = -2.529822128 + -1 Combine like terms: -2.529822128 + -1 = -3.529822128 x = -3.529822128 Simplifying x = -3.529822128Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.529822128, -3.529822128}
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