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Simplifying 3x(x) + -19 = 37 + -1(x) Multiply x * x 3x2 + -19 = 37 + -1(x) Reorder the terms: -19 + 3x2 = 37 + -1(x) Solving -19 + 3x2 = 37 + -1x Solving for variable 'x'. Reorder the terms: -19 + -37 + x + 3x2 = 37 + -1x + -37 + x Combine like terms: -19 + -37 = -56 -56 + x + 3x2 = 37 + -1x + -37 + x Reorder the terms: -56 + x + 3x2 = 37 + -37 + -1x + x Combine like terms: 37 + -37 = 0 -56 + x + 3x2 = 0 + -1x + x -56 + x + 3x2 = -1x + x Combine like terms: -1x + x = 0 -56 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -18.66666667 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '18.66666667' to each side of the equation. -18.66666667 + 0.3333333333x + 18.66666667 + x2 = 0 + 18.66666667 Reorder the terms: -18.66666667 + 18.66666667 + 0.3333333333x + x2 = 0 + 18.66666667 Combine like terms: -18.66666667 + 18.66666667 = 0.00000000 0.00000000 + 0.3333333333x + x2 = 0 + 18.66666667 0.3333333333x + x2 = 0 + 18.66666667 Combine like terms: 0 + 18.66666667 = 18.66666667 0.3333333333x + x2 = 18.66666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 18.66666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 18.66666667 + 0.25 Combine like terms: 18.66666667 + 0.25 = 18.91666667 0.25 + 0.3333333333x + x2 = 18.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 18.91666667 Calculate the square root of the right side: 4.349329451 Break this problem into two subproblems by setting (x + 0.5) equal to 4.349329451 and -4.349329451.Subproblem 1
x + 0.5 = 4.349329451 Simplifying x + 0.5 = 4.349329451 Reorder the terms: 0.5 + x = 4.349329451 Solving 0.5 + x = 4.349329451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.349329451 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.349329451 + -0.5 x = 4.349329451 + -0.5 Combine like terms: 4.349329451 + -0.5 = 3.849329451 x = 3.849329451 Simplifying x = 3.849329451Subproblem 2
x + 0.5 = -4.349329451 Simplifying x + 0.5 = -4.349329451 Reorder the terms: 0.5 + x = -4.349329451 Solving 0.5 + x = -4.349329451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.349329451 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.349329451 + -0.5 x = -4.349329451 + -0.5 Combine like terms: -4.349329451 + -0.5 = -4.849329451 x = -4.849329451 Simplifying x = -4.849329451Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.849329451, -4.849329451}
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