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Simplifying 4x2 + 6x + -27 = 0 Reorder the terms: -27 + 6x + 4x2 = 0 Solving -27 + 6x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + 1.5x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + 1.5x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + 1.5x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + 1.5x + x2 = 0 + 6.75 1.5x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 1.5x + x2 = 6.75 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 6.75 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 6.75 + 0.5625 Combine like terms: 6.75 + 0.5625 = 7.3125 0.5625 + 1.5x + x2 = 7.3125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 7.3125 Calculate the square root of the right side: 2.704163457 Break this problem into two subproblems by setting (x + 0.75) equal to 2.704163457 and -2.704163457.Subproblem 1
x + 0.75 = 2.704163457 Simplifying x + 0.75 = 2.704163457 Reorder the terms: 0.75 + x = 2.704163457 Solving 0.75 + x = 2.704163457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.704163457 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.704163457 + -0.75 x = 2.704163457 + -0.75 Combine like terms: 2.704163457 + -0.75 = 1.954163457 x = 1.954163457 Simplifying x = 1.954163457Subproblem 2
x + 0.75 = -2.704163457 Simplifying x + 0.75 = -2.704163457 Reorder the terms: 0.75 + x = -2.704163457 Solving 0.75 + x = -2.704163457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.704163457 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.704163457 + -0.75 x = -2.704163457 + -0.75 Combine like terms: -2.704163457 + -0.75 = -3.454163457 x = -3.454163457 Simplifying x = -3.454163457Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.954163457, -3.454163457}
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