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Simplifying 0 = 0.3x2 + 2x + -189 Reorder the terms: 0 = -189 + 2x + 0.3x2 Solving 0 = -189 + 2x + 0.3x2 Solving for variable 'x'. Combine like terms: 0 + 189 = 189 189 + -2x + -0.3x2 = -189 + 2x + 0.3x2 + 189 + -2x + -0.3x2 Reorder the terms: 189 + -2x + -0.3x2 = -189 + 189 + 2x + -2x + 0.3x2 + -0.3x2 Combine like terms: -189 + 189 = 0 189 + -2x + -0.3x2 = 0 + 2x + -2x + 0.3x2 + -0.3x2 189 + -2x + -0.3x2 = 2x + -2x + 0.3x2 + -0.3x2 Combine like terms: 2x + -2x = 0 189 + -2x + -0.3x2 = 0 + 0.3x2 + -0.3x2 189 + -2x + -0.3x2 = 0.3x2 + -0.3x2 Combine like terms: 0.3x2 + -0.3x2 = 0.0 189 + -2x + -0.3x2 = 0.0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. -630 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '630' to each side of the equation. -630 + 6.666666667x + 630 + x2 = 0 + 630 Reorder the terms: -630 + 630 + 6.666666667x + x2 = 0 + 630 Combine like terms: -630 + 630 = 0 0 + 6.666666667x + x2 = 0 + 630 6.666666667x + x2 = 0 + 630 Combine like terms: 0 + 630 = 630 6.666666667x + x2 = 630 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 = 630 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 630 + 11.11111112 Combine like terms: 630 + 11.11111112 = 641.11111112 11.11111112 + 6.666666667x + x2 = 641.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 641.11111112 Calculate the square root of the right side: 25.32017202 Break this problem into two subproblems by setting (x + 3.333333334) equal to 25.32017202 and -25.32017202.Subproblem 1
x + 3.333333334 = 25.32017202 Simplifying x + 3.333333334 = 25.32017202 Reorder the terms: 3.333333334 + x = 25.32017202 Solving 3.333333334 + x = 25.32017202 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 = 25.32017202 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 25.32017202 + -3.333333334 x = 25.32017202 + -3.333333334 Combine like terms: 25.32017202 + -3.333333334 = 21.986838686 x = 21.986838686 Simplifying x = 21.986838686Subproblem 2
x + 3.333333334 = -25.32017202 Simplifying x + 3.333333334 = -25.32017202 Reorder the terms: 3.333333334 + x = -25.32017202 Solving 3.333333334 + x = -25.32017202 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 = -25.32017202 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -25.32017202 + -3.333333334 x = -25.32017202 + -3.333333334 Combine like terms: -25.32017202 + -3.333333334 = -28.653505354 x = -28.653505354 Simplifying x = -28.653505354Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.986838686, -28.653505354}
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