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Simplifying 0.3x2 + -8x + 4 = 0 Reorder the terms: 4 + -8x + 0.3x2 = 0 Solving 4 + -8x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 13.33333333 + -26.66666667x + x2 = 0 Move the constant term to the right: Add '-13.33333333' to each side of the equation. 13.33333333 + -26.66666667x + -13.33333333 + x2 = 0 + -13.33333333 Reorder the terms: 13.33333333 + -13.33333333 + -26.66666667x + x2 = 0 + -13.33333333 Combine like terms: 13.33333333 + -13.33333333 = 0.00000000 0.00000000 + -26.66666667x + x2 = 0 + -13.33333333 -26.66666667x + x2 = 0 + -13.33333333 Combine like terms: 0 + -13.33333333 = -13.33333333 -26.66666667x + x2 = -13.33333333 The x term is -26.66666667x. Take half its coefficient (-13.33333334). Square it (177.7777780) and add it to both sides. Add '177.7777780' to each side of the equation. -26.66666667x + 177.7777780 + x2 = -13.33333333 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667x + x2 = -13.33333333 + 177.7777780 Combine like terms: -13.33333333 + 177.7777780 = 164.44444467 177.7777780 + -26.66666667x + x2 = 164.44444467 Factor a perfect square on the left side: (x + -13.33333334)(x + -13.33333334) = 164.44444467 Calculate the square root of the right side: 12.823589383 Break this problem into two subproblems by setting (x + -13.33333334) equal to 12.823589383 and -12.823589383.Subproblem 1
x + -13.33333334 = 12.823589383 Simplifying x + -13.33333334 = 12.823589383 Reorder the terms: -13.33333334 + x = 12.823589383 Solving -13.33333334 + x = 12.823589383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + x = 12.823589383 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = 12.823589383 + 13.33333334 x = 12.823589383 + 13.33333334 Combine like terms: 12.823589383 + 13.33333334 = 26.156922723 x = 26.156922723 Simplifying x = 26.156922723Subproblem 2
x + -13.33333334 = -12.823589383 Simplifying x + -13.33333334 = -12.823589383 Reorder the terms: -13.33333334 + x = -12.823589383 Solving -13.33333334 + x = -12.823589383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + x = -12.823589383 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = -12.823589383 + 13.33333334 x = -12.823589383 + 13.33333334 Combine like terms: -12.823589383 + 13.33333334 = 0.509743957 x = 0.509743957 Simplifying x = 0.509743957Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.156922723, 0.509743957}
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