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Simplifying 5x2 + -30x + -36 = 0 Reorder the terms: -36 + -30x + 5x2 = 0 Solving -36 + -30x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + -6x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + -6x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + -6x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + -6x + x2 = 0 + 7.2 -6x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 -6x + x2 = 7.2 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 = 7.2 + 9 Reorder the terms: 9 + -6x + x2 = 7.2 + 9 Combine like terms: 7.2 + 9 = 16.2 9 + -6x + x2 = 16.2 Factor a perfect square on the left side: (x + -3)(x + -3) = 16.2 Calculate the square root of the right side: 4.02492236 Break this problem into two subproblems by setting (x + -3) equal to 4.02492236 and -4.02492236.Subproblem 1
x + -3 = 4.02492236 Simplifying x + -3 = 4.02492236 Reorder the terms: -3 + x = 4.02492236 Solving -3 + x = 4.02492236 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 = 4.02492236 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.02492236 + 3 x = 4.02492236 + 3 Combine like terms: 4.02492236 + 3 = 7.02492236 x = 7.02492236 Simplifying x = 7.02492236Subproblem 2
x + -3 = -4.02492236 Simplifying x + -3 = -4.02492236 Reorder the terms: -3 + x = -4.02492236 Solving -3 + x = -4.02492236 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 = -4.02492236 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.02492236 + 3 x = -4.02492236 + 3 Combine like terms: -4.02492236 + 3 = -1.02492236 x = -1.02492236 Simplifying x = -1.02492236Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.02492236, -1.02492236}
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