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Simplifying 2x2 + -66x = 7x2 + -4x + -48 Reorder the terms: -66x + 2x2 = 7x2 + -4x + -48 Reorder the terms: -66x + 2x2 = -48 + -4x + 7x2 Solving -66x + 2x2 = -48 + -4x + 7x2 Solving for variable 'x'. Reorder the terms: 48 + -66x + 4x + 2x2 + -7x2 = -48 + -4x + 7x2 + 48 + 4x + -7x2 Combine like terms: -66x + 4x = -62x 48 + -62x + 2x2 + -7x2 = -48 + -4x + 7x2 + 48 + 4x + -7x2 Combine like terms: 2x2 + -7x2 = -5x2 48 + -62x + -5x2 = -48 + -4x + 7x2 + 48 + 4x + -7x2 Reorder the terms: 48 + -62x + -5x2 = -48 + 48 + -4x + 4x + 7x2 + -7x2 Combine like terms: -48 + 48 = 0 48 + -62x + -5x2 = 0 + -4x + 4x + 7x2 + -7x2 48 + -62x + -5x2 = -4x + 4x + 7x2 + -7x2 Combine like terms: -4x + 4x = 0 48 + -62x + -5x2 = 0 + 7x2 + -7x2 48 + -62x + -5x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 48 + -62x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -9.6 + 12.4x + x2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + 12.4x + 9.6 + x2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + 12.4x + x2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + 12.4x + x2 = 0 + 9.6 12.4x + x2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 12.4x + x2 = 9.6 The x term is 12.4x. Take half its coefficient (6.2). Square it (38.44) and add it to both sides. Add '38.44' to each side of the equation. 12.4x + 38.44 + x2 = 9.6 + 38.44 Reorder the terms: 38.44 + 12.4x + x2 = 9.6 + 38.44 Combine like terms: 9.6 + 38.44 = 48.04 38.44 + 12.4x + x2 = 48.04 Factor a perfect square on the left side: (x + 6.2)(x + 6.2) = 48.04 Calculate the square root of the right side: 6.93108938 Break this problem into two subproblems by setting (x + 6.2) equal to 6.93108938 and -6.93108938.Subproblem 1
x + 6.2 = 6.93108938 Simplifying x + 6.2 = 6.93108938 Reorder the terms: 6.2 + x = 6.93108938 Solving 6.2 + x = 6.93108938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.2' to each side of the equation. 6.2 + -6.2 + x = 6.93108938 + -6.2 Combine like terms: 6.2 + -6.2 = 0.0 0.0 + x = 6.93108938 + -6.2 x = 6.93108938 + -6.2 Combine like terms: 6.93108938 + -6.2 = 0.73108938 x = 0.73108938 Simplifying x = 0.73108938Subproblem 2
x + 6.2 = -6.93108938 Simplifying x + 6.2 = -6.93108938 Reorder the terms: 6.2 + x = -6.93108938 Solving 6.2 + x = -6.93108938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.2' to each side of the equation. 6.2 + -6.2 + x = -6.93108938 + -6.2 Combine like terms: 6.2 + -6.2 = 0.0 0.0 + x = -6.93108938 + -6.2 x = -6.93108938 + -6.2 Combine like terms: -6.93108938 + -6.2 = -13.13108938 x = -13.13108938 Simplifying x = -13.13108938Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.73108938, -13.13108938}
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