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Simplifying 6x2 + -28x + 15 = 0 Reorder the terms: 15 + -28x + 6x2 = 0 Solving 15 + -28x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.5 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -4.666666667x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -4.666666667x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -4.666666667x + x2 = 0 + -2.5 -4.666666667x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -4.666666667x + x2 = -2.5 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = -2.5 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = -2.5 + 5.444444448 Combine like terms: -2.5 + 5.444444448 = 2.944444448 5.444444448 + -4.666666667x + x2 = 2.944444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 2.944444448 Calculate the square root of the right side: 1.715938358 Break this problem into two subproblems by setting (x + -2.333333334) equal to 1.715938358 and -1.715938358.Subproblem 1
x + -2.333333334 = 1.715938358 Simplifying x + -2.333333334 = 1.715938358 Reorder the terms: -2.333333334 + x = 1.715938358 Solving -2.333333334 + x = 1.715938358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 1.715938358 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 1.715938358 + 2.333333334 x = 1.715938358 + 2.333333334 Combine like terms: 1.715938358 + 2.333333334 = 4.049271692 x = 4.049271692 Simplifying x = 4.049271692Subproblem 2
x + -2.333333334 = -1.715938358 Simplifying x + -2.333333334 = -1.715938358 Reorder the terms: -2.333333334 + x = -1.715938358 Solving -2.333333334 + x = -1.715938358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -1.715938358 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -1.715938358 + 2.333333334 x = -1.715938358 + 2.333333334 Combine like terms: -1.715938358 + 2.333333334 = 0.617394976 x = 0.617394976 Simplifying x = 0.617394976Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.049271692, 0.617394976}
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