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Simplifying 4x2 + 3x + -12 = 6x2 + -7 + -60 Reorder the terms: -12 + 3x + 4x2 = 6x2 + -7 + -60 Reorder the terms: -12 + 3x + 4x2 = -7 + -60 + 6x2 Combine like terms: -7 + -60 = -67 -12 + 3x + 4x2 = -67 + 6x2 Solving -12 + 3x + 4x2 = -67 + 6x2 Solving for variable 'x'. Reorder the terms: -12 + 67 + 3x + 4x2 + -6x2 = -67 + 6x2 + 67 + -6x2 Combine like terms: -12 + 67 = 55 55 + 3x + 4x2 + -6x2 = -67 + 6x2 + 67 + -6x2 Combine like terms: 4x2 + -6x2 = -2x2 55 + 3x + -2x2 = -67 + 6x2 + 67 + -6x2 Reorder the terms: 55 + 3x + -2x2 = -67 + 67 + 6x2 + -6x2 Combine like terms: -67 + 67 = 0 55 + 3x + -2x2 = 0 + 6x2 + -6x2 55 + 3x + -2x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 55 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -27.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + -1.5x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + -1.5x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + -1.5x + x2 = 0 + 27.5 -1.5x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 -1.5x + x2 = 27.5 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 = 27.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 27.5 + 0.5625 Combine like terms: 27.5 + 0.5625 = 28.0625 0.5625 + -1.5x + x2 = 28.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 28.0625 Calculate the square root of the right side: 5.297405025 Break this problem into two subproblems by setting (x + -0.75) equal to 5.297405025 and -5.297405025.Subproblem 1
x + -0.75 = 5.297405025 Simplifying x + -0.75 = 5.297405025 Reorder the terms: -0.75 + x = 5.297405025 Solving -0.75 + x = 5.297405025 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 = 5.297405025 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 5.297405025 + 0.75 x = 5.297405025 + 0.75 Combine like terms: 5.297405025 + 0.75 = 6.047405025 x = 6.047405025 Simplifying x = 6.047405025Subproblem 2
x + -0.75 = -5.297405025 Simplifying x + -0.75 = -5.297405025 Reorder the terms: -0.75 + x = -5.297405025 Solving -0.75 + x = -5.297405025 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 = -5.297405025 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -5.297405025 + 0.75 x = -5.297405025 + 0.75 Combine like terms: -5.297405025 + 0.75 = -4.547405025 x = -4.547405025 Simplifying x = -4.547405025Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.047405025, -4.547405025}
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