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Simplifying x = 5x2 + -2x + -7 Reorder the terms: x = -7 + -2x + 5x2 Solving x = -7 + -2x + 5x2 Solving for variable 'x'. Reorder the terms: 7 + x + 2x + -5x2 = -7 + -2x + 5x2 + 7 + 2x + -5x2 Combine like terms: x + 2x = 3x 7 + 3x + -5x2 = -7 + -2x + 5x2 + 7 + 2x + -5x2 Reorder the terms: 7 + 3x + -5x2 = -7 + 7 + -2x + 2x + 5x2 + -5x2 Combine like terms: -7 + 7 = 0 7 + 3x + -5x2 = 0 + -2x + 2x + 5x2 + -5x2 7 + 3x + -5x2 = -2x + 2x + 5x2 + -5x2 Combine like terms: -2x + 2x = 0 7 + 3x + -5x2 = 0 + 5x2 + -5x2 7 + 3x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 7 + 3x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.4 + -0.6x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.6x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.6x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.6x + x2 = 0 + 1.4 -0.6x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.6x + x2 = 1.4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 1.4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 1.4 + 0.09 Combine like terms: 1.4 + 0.09 = 1.49 0.09 + -0.6x + x2 = 1.49 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 1.49 Calculate the square root of the right side: 1.220655562 Break this problem into two subproblems by setting (x + -0.3) equal to 1.220655562 and -1.220655562.Subproblem 1
x + -0.3 = 1.220655562 Simplifying x + -0.3 = 1.220655562 Reorder the terms: -0.3 + x = 1.220655562 Solving -0.3 + x = 1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.220655562 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.220655562 + 0.3 x = 1.220655562 + 0.3 Combine like terms: 1.220655562 + 0.3 = 1.520655562 x = 1.520655562 Simplifying x = 1.520655562Subproblem 2
x + -0.3 = -1.220655562 Simplifying x + -0.3 = -1.220655562 Reorder the terms: -0.3 + x = -1.220655562 Solving -0.3 + x = -1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.220655562 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.220655562 + 0.3 x = -1.220655562 + 0.3 Combine like terms: -1.220655562 + 0.3 = -0.920655562 x = -0.920655562 Simplifying x = -0.920655562Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.520655562, -0.920655562}
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