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Simplifying 5x2 + 40x + -27 = 0 Reorder the terms: -27 + 40x + 5x2 = 0 Solving -27 + 40x + 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 + 8x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 8x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 8x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 8x + x2 = 0 + 5.4 8x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 8x + x2 = 5.4 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 5.4 + 16 Reorder the terms: 16 + 8x + x2 = 5.4 + 16 Combine like terms: 5.4 + 16 = 21.4 16 + 8x + x2 = 21.4 Factor a perfect square on the left side: (x + 4)(x + 4) = 21.4 Calculate the square root of the right side: 4.626013402 Break this problem into two subproblems by setting (x + 4) equal to 4.626013402 and -4.626013402.Subproblem 1
x + 4 = 4.626013402 Simplifying x + 4 = 4.626013402 Reorder the terms: 4 + x = 4.626013402 Solving 4 + x = 4.626013402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.626013402 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.626013402 + -4 x = 4.626013402 + -4 Combine like terms: 4.626013402 + -4 = 0.626013402 x = 0.626013402 Simplifying x = 0.626013402Subproblem 2
x + 4 = -4.626013402 Simplifying x + 4 = -4.626013402 Reorder the terms: 4 + x = -4.626013402 Solving 4 + x = -4.626013402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.626013402 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.626013402 + -4 x = -4.626013402 + -4 Combine like terms: -4.626013402 + -4 = -8.626013402 x = -8.626013402 Simplifying x = -8.626013402Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.626013402, -8.626013402}
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