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Simplifying 5x2 + -30x = -21 Reorder the terms: -30x + 5x2 = -21 Solving -30x + 5x2 = -21 Solving for variable 'x'. Reorder the terms: 21 + -30x + 5x2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + -30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.2 + -6x + x2 = 0 Move the constant term to the right: Add '-4.2' to each side of the equation. 4.2 + -6x + -4.2 + x2 = 0 + -4.2 Reorder the terms: 4.2 + -4.2 + -6x + x2 = 0 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + -6x + x2 = 0 + -4.2 -6x + x2 = 0 + -4.2 Combine like terms: 0 + -4.2 = -4.2 -6x + x2 = -4.2 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -4.2 + 9 Reorder the terms: 9 + -6x + x2 = -4.2 + 9 Combine like terms: -4.2 + 9 = 4.8 9 + -6x + x2 = 4.8 Factor a perfect square on the left side: (x + -3)(x + -3) = 4.8 Calculate the square root of the right side: 2.19089023 Break this problem into two subproblems by setting (x + -3) equal to 2.19089023 and -2.19089023.Subproblem 1
x + -3 = 2.19089023 Simplifying x + -3 = 2.19089023 Reorder the terms: -3 + x = 2.19089023 Solving -3 + x = 2.19089023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.19089023 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.19089023 + 3 x = 2.19089023 + 3 Combine like terms: 2.19089023 + 3 = 5.19089023 x = 5.19089023 Simplifying x = 5.19089023Subproblem 2
x + -3 = -2.19089023 Simplifying x + -3 = -2.19089023 Reorder the terms: -3 + x = -2.19089023 Solving -3 + x = -2.19089023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.19089023 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.19089023 + 3 x = -2.19089023 + 3 Combine like terms: -2.19089023 + 3 = 0.80910977 x = 0.80910977 Simplifying x = 0.80910977Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.19089023, 0.80910977}
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