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Simplifying 5x2 + -13x = 30 Reorder the terms: -13x + 5x2 = 30 Solving -13x + 5x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + -13x + 5x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -13x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6 + -2.6x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2.6x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -2.6x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2.6x + x2 = 0 + 6 -2.6x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2.6x + x2 = 6 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 = 6 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = 6 + 1.69 Combine like terms: 6 + 1.69 = 7.69 1.69 + -2.6x + x2 = 7.69 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 7.69 Calculate the square root of the right side: 2.773084925 Break this problem into two subproblems by setting (x + -1.3) equal to 2.773084925 and -2.773084925.Subproblem 1
x + -1.3 = 2.773084925 Simplifying x + -1.3 = 2.773084925 Reorder the terms: -1.3 + x = 2.773084925 Solving -1.3 + x = 2.773084925 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 = 2.773084925 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 2.773084925 + 1.3 x = 2.773084925 + 1.3 Combine like terms: 2.773084925 + 1.3 = 4.073084925 x = 4.073084925 Simplifying x = 4.073084925Subproblem 2
x + -1.3 = -2.773084925 Simplifying x + -1.3 = -2.773084925 Reorder the terms: -1.3 + x = -2.773084925 Solving -1.3 + x = -2.773084925 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 = -2.773084925 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -2.773084925 + 1.3 x = -2.773084925 + 1.3 Combine like terms: -2.773084925 + 1.3 = -1.473084925 x = -1.473084925 Simplifying x = -1.473084925Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.073084925, -1.473084925}
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