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Simplifying 5x2 + 30x = -42 Reorder the terms: 30x + 5x2 = -42 Solving 30x + 5x2 = -42 Solving for variable 'x'. Reorder the terms: 42 + 30x + 5x2 = -42 + 42 Combine like terms: -42 + 42 = 0 42 + 30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8.4 + 6x + x2 = 0 Move the constant term to the right: Add '-8.4' to each side of the equation. 8.4 + 6x + -8.4 + x2 = 0 + -8.4 Reorder the terms: 8.4 + -8.4 + 6x + x2 = 0 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + 6x + x2 = 0 + -8.4 6x + x2 = 0 + -8.4 Combine like terms: 0 + -8.4 = -8.4 6x + x2 = -8.4 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 = -8.4 + 9 Reorder the terms: 9 + 6x + x2 = -8.4 + 9 Combine like terms: -8.4 + 9 = 0.6 9 + 6x + x2 = 0.6 Factor a perfect square on the left side: (x + 3)(x + 3) = 0.6 Calculate the square root of the right side: 0.774596669 Break this problem into two subproblems by setting (x + 3) equal to 0.774596669 and -0.774596669.Subproblem 1
x + 3 = 0.774596669 Simplifying x + 3 = 0.774596669 Reorder the terms: 3 + x = 0.774596669 Solving 3 + x = 0.774596669 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 = 0.774596669 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0.774596669 + -3 x = 0.774596669 + -3 Combine like terms: 0.774596669 + -3 = -2.225403331 x = -2.225403331 Simplifying x = -2.225403331Subproblem 2
x + 3 = -0.774596669 Simplifying x + 3 = -0.774596669 Reorder the terms: 3 + x = -0.774596669 Solving 3 + x = -0.774596669 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 = -0.774596669 + -3 Combine like terms: 3 + -3 = 0 0 + x = -0.774596669 + -3 x = -0.774596669 + -3 Combine like terms: -0.774596669 + -3 = -3.774596669 x = -3.774596669 Simplifying x = -3.774596669Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.225403331, -3.774596669}
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