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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 = -0.617394976 x = -0.617394976 Simplifying x = -0.617394976Subproblem 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 = -4.049271692 x = -4.049271692 Simplifying x = -4.049271692Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.617394976, -4.049271692}
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