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Simplifying 5x2 + -13x + -28 = 8 Reorder the terms: -28 + -13x + 5x2 = 8 Solving -28 + -13x + 5x2 = 8 Solving for variable 'x'. Reorder the terms: -28 + -8 + -13x + 5x2 = 8 + -8 Combine like terms: -28 + -8 = -36 -36 + -13x + 5x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -36 + -13x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + -2.6x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + -2.6x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + -2.6x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + -2.6x + x2 = 0 + 7.2 -2.6x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 -2.6x + x2 = 7.2 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = 7.2 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = 7.2 + 1.69 Combine like terms: 7.2 + 1.69 = 8.89 1.69 + -2.6x + x2 = 8.89 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 8.89 Calculate the square root of the right side: 2.981610303 Break this problem into two subproblems by setting (x + -1.3) equal to 2.981610303 and -2.981610303.Subproblem 1
x + -1.3 = 2.981610303 Simplifying x + -1.3 = 2.981610303 Reorder the terms: -1.3 + x = 2.981610303 Solving -1.3 + x = 2.981610303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 2.981610303 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 2.981610303 + 1.3 x = 2.981610303 + 1.3 Combine like terms: 2.981610303 + 1.3 = 4.281610303 x = 4.281610303 Simplifying x = 4.281610303Subproblem 2
x + -1.3 = -2.981610303 Simplifying x + -1.3 = -2.981610303 Reorder the terms: -1.3 + x = -2.981610303 Solving -1.3 + x = -2.981610303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = -2.981610303 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -2.981610303 + 1.3 x = -2.981610303 + 1.3 Combine like terms: -2.981610303 + 1.3 = -1.681610303 x = -1.681610303 Simplifying x = -1.681610303Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.281610303, -1.681610303}
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