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Simplifying 0 = 0.213x2 + -0.862x + 0.75 Reorder the terms: 0 = 0.75 + -0.862x + 0.213x2 Solving 0 = 0.75 + -0.862x + 0.213x2 Solving for variable 'x'. Combine like terms: 0 + -0.75 = -0.75 -0.75 + 0.862x + -0.213x2 = 0.75 + -0.862x + 0.213x2 + -0.75 + 0.862x + -0.213x2 Reorder the terms: -0.75 + 0.862x + -0.213x2 = 0.75 + -0.75 + -0.862x + 0.862x + 0.213x2 + -0.213x2 Combine like terms: 0.75 + -0.75 = 0.00 -0.75 + 0.862x + -0.213x2 = 0.00 + -0.862x + 0.862x + 0.213x2 + -0.213x2 -0.75 + 0.862x + -0.213x2 = -0.862x + 0.862x + 0.213x2 + -0.213x2 Combine like terms: -0.862x + 0.862x = 0.000 -0.75 + 0.862x + -0.213x2 = 0.000 + 0.213x2 + -0.213x2 -0.75 + 0.862x + -0.213x2 = 0.213x2 + -0.213x2 Combine like terms: 0.213x2 + -0.213x2 = 0.000 -0.75 + 0.862x + -0.213x2 = 0.000 Begin completing the square. Divide all terms by -0.213 the coefficient of the squared term: Divide each side by '-0.213'. 3.521126761 + -4.046948357x + x2 = 0 Move the constant term to the right: Add '-3.521126761' to each side of the equation. 3.521126761 + -4.046948357x + -3.521126761 + x2 = 0 + -3.521126761 Reorder the terms: 3.521126761 + -3.521126761 + -4.046948357x + x2 = 0 + -3.521126761 Combine like terms: 3.521126761 + -3.521126761 = 0.000000000 0.000000000 + -4.046948357x + x2 = 0 + -3.521126761 -4.046948357x + x2 = 0 + -3.521126761 Combine like terms: 0 + -3.521126761 = -3.521126761 -4.046948357x + x2 = -3.521126761 The x term is -4.046948357x. Take half its coefficient (-2.023474179). Square it (4.094447753) and add it to both sides. Add '4.094447753' to each side of the equation. -4.046948357x + 4.094447753 + x2 = -3.521126761 + 4.094447753 Reorder the terms: 4.094447753 + -4.046948357x + x2 = -3.521126761 + 4.094447753 Combine like terms: -3.521126761 + 4.094447753 = 0.573320992 4.094447753 + -4.046948357x + x2 = 0.573320992 Factor a perfect square on the left side: (x + -2.023474179)(x + -2.023474179) = 0.573320992 Calculate the square root of the right side: 0.75717963 Break this problem into two subproblems by setting (x + -2.023474179) equal to 0.75717963 and -0.75717963.Subproblem 1
x + -2.023474179 = 0.75717963 Simplifying x + -2.023474179 = 0.75717963 Reorder the terms: -2.023474179 + x = 0.75717963 Solving -2.023474179 + x = 0.75717963 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.023474179' to each side of the equation. -2.023474179 + 2.023474179 + x = 0.75717963 + 2.023474179 Combine like terms: -2.023474179 + 2.023474179 = 0.000000000 0.000000000 + x = 0.75717963 + 2.023474179 x = 0.75717963 + 2.023474179 Combine like terms: 0.75717963 + 2.023474179 = 2.780653809 x = 2.780653809 Simplifying x = 2.780653809Subproblem 2
x + -2.023474179 = -0.75717963 Simplifying x + -2.023474179 = -0.75717963 Reorder the terms: -2.023474179 + x = -0.75717963 Solving -2.023474179 + x = -0.75717963 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.023474179' to each side of the equation. -2.023474179 + 2.023474179 + x = -0.75717963 + 2.023474179 Combine like terms: -2.023474179 + 2.023474179 = 0.000000000 0.000000000 + x = -0.75717963 + 2.023474179 x = -0.75717963 + 2.023474179 Combine like terms: -0.75717963 + 2.023474179 = 1.266294549 x = 1.266294549 Simplifying x = 1.266294549Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.780653809, 1.266294549}
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