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Simplifying 0 = -5x2 + -30x + 51 Reorder the terms: 0 = 51 + -30x + -5x2 Solving 0 = 51 + -30x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -51 = -51 -51 + 30x + 5x2 = 51 + -30x + -5x2 + -51 + 30x + 5x2 Reorder the terms: -51 + 30x + 5x2 = 51 + -51 + -30x + 30x + -5x2 + 5x2 Combine like terms: 51 + -51 = 0 -51 + 30x + 5x2 = 0 + -30x + 30x + -5x2 + 5x2 -51 + 30x + 5x2 = -30x + 30x + -5x2 + 5x2 Combine like terms: -30x + 30x = 0 -51 + 30x + 5x2 = 0 + -5x2 + 5x2 -51 + 30x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -51 + 30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.2 + 6x + x2 = 0 Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + 6x + 10.2 + x2 = 0 + 10.2 Reorder the terms: -10.2 + 10.2 + 6x + x2 = 0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + 6x + x2 = 0 + 10.2 6x + x2 = 0 + 10.2 Combine like terms: 0 + 10.2 = 10.2 6x + x2 = 10.2 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 = 10.2 + 9 Reorder the terms: 9 + 6x + x2 = 10.2 + 9 Combine like terms: 10.2 + 9 = 19.2 9 + 6x + x2 = 19.2 Factor a perfect square on the left side: (x + 3)(x + 3) = 19.2 Calculate the square root of the right side: 4.38178046 Break this problem into two subproblems by setting (x + 3) equal to 4.38178046 and -4.38178046.Subproblem 1
x + 3 = 4.38178046 Simplifying x + 3 = 4.38178046 Reorder the terms: 3 + x = 4.38178046 Solving 3 + x = 4.38178046 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 = 4.38178046 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.38178046 + -3 x = 4.38178046 + -3 Combine like terms: 4.38178046 + -3 = 1.38178046 x = 1.38178046 Simplifying x = 1.38178046Subproblem 2
x + 3 = -4.38178046 Simplifying x + 3 = -4.38178046 Reorder the terms: 3 + x = -4.38178046 Solving 3 + x = -4.38178046 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 = -4.38178046 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.38178046 + -3 x = -4.38178046 + -3 Combine like terms: -4.38178046 + -3 = -7.38178046 x = -7.38178046 Simplifying x = -7.38178046Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.38178046, -7.38178046}
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