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Simplifying -0.3x2 + 0.5x + 6 = x Reorder the terms: 6 + 0.5x + -0.3x2 = x Solving 6 + 0.5x + -0.3x2 = x Solving for variable 'x'. Reorder the terms: 6 + 0.5x + -1x + -0.3x2 = x + -1x Combine like terms: 0.5x + -1x = -0.5x 6 + -0.5x + -0.3x2 = x + -1x Combine like terms: x + -1x = 0 6 + -0.5x + -0.3x2 = 0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. -20 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 1.666666667x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 1.666666667x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 1.666666667x + x2 = 0 + 20 1.666666667x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 1.666666667x + x2 = 20 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 20 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 20 + 0.6944444447 Combine like terms: 20 + 0.6944444447 = 20.6944444447 0.6944444447 + 1.666666667x + x2 = 20.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 20.6944444447 Calculate the square root of the right side: 4.549114688 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 4.549114688 and -4.549114688.Subproblem 1
x + 0.8333333335 = 4.549114688 Simplifying x + 0.8333333335 = 4.549114688 Reorder the terms: 0.8333333335 + x = 4.549114688 Solving 0.8333333335 + x = 4.549114688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 4.549114688 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 4.549114688 + -0.8333333335 x = 4.549114688 + -0.8333333335 Combine like terms: 4.549114688 + -0.8333333335 = 3.7157813545 x = 3.7157813545 Simplifying x = 3.7157813545Subproblem 2
x + 0.8333333335 = -4.549114688 Simplifying x + 0.8333333335 = -4.549114688 Reorder the terms: 0.8333333335 + x = -4.549114688 Solving 0.8333333335 + x = -4.549114688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -4.549114688 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -4.549114688 + -0.8333333335 x = -4.549114688 + -0.8333333335 Combine like terms: -4.549114688 + -0.8333333335 = -5.3824480215 x = -5.3824480215 Simplifying x = -5.3824480215Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.7157813545, -5.3824480215}
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