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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 = 8.626013402 x = 8.626013402 Simplifying x = 8.626013402Subproblem 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 = -0.626013402 x = -0.626013402 Simplifying x = -0.626013402Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.626013402, -0.626013402}
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