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Simplifying 0.3x2 + -2x = 15 Reorder the terms: -2x + 0.3x2 = 15 Solving -2x + 0.3x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -2x + 0.3x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -2x + 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'. -50 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -6.666666667x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -6.666666667x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -6.666666667x + x2 = 0 + 50 -6.666666667x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -6.666666667x + x2 = 50 The x term is -6.666666667x. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667x + 11.11111112 + x2 = 50 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = 50 + 11.11111112 Combine like terms: 50 + 11.11111112 = 61.11111112 11.11111112 + -6.666666667x + x2 = 61.11111112 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 61.11111112 Calculate the square root of the right side: 7.8173596 Break this problem into two subproblems by setting (x + -3.333333334) equal to 7.8173596 and -7.8173596.Subproblem 1
x + -3.333333334 = 7.8173596 Simplifying x + -3.333333334 = 7.8173596 Reorder the terms: -3.333333334 + x = 7.8173596 Solving -3.333333334 + x = 7.8173596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = 7.8173596 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 7.8173596 + 3.333333334 x = 7.8173596 + 3.333333334 Combine like terms: 7.8173596 + 3.333333334 = 11.150692934 x = 11.150692934 Simplifying x = 11.150692934Subproblem 2
x + -3.333333334 = -7.8173596 Simplifying x + -3.333333334 = -7.8173596 Reorder the terms: -3.333333334 + x = -7.8173596 Solving -3.333333334 + x = -7.8173596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = -7.8173596 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -7.8173596 + 3.333333334 x = -7.8173596 + 3.333333334 Combine like terms: -7.8173596 + 3.333333334 = -4.484026266 x = -4.484026266 Simplifying x = -4.484026266Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.150692934, -4.484026266}
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