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Simplifying 10x2 + 60x = 89 Reorder the terms: 60x + 10x2 = 89 Solving 60x + 10x2 = 89 Solving for variable 'x'. Reorder the terms: -89 + 60x + 10x2 = 89 + -89 Combine like terms: 89 + -89 = 0 -89 + 60x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -8.9 + 6x + x2 = 0 Move the constant term to the right: Add '8.9' to each side of the equation. -8.9 + 6x + 8.9 + x2 = 0 + 8.9 Reorder the terms: -8.9 + 8.9 + 6x + x2 = 0 + 8.9 Combine like terms: -8.9 + 8.9 = 0.0 0.0 + 6x + x2 = 0 + 8.9 6x + x2 = 0 + 8.9 Combine like terms: 0 + 8.9 = 8.9 6x + x2 = 8.9 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 = 8.9 + 9 Reorder the terms: 9 + 6x + x2 = 8.9 + 9 Combine like terms: 8.9 + 9 = 17.9 9 + 6x + x2 = 17.9 Factor a perfect square on the left side: (x + 3)(x + 3) = 17.9 Calculate the square root of the right side: 4.23083916 Break this problem into two subproblems by setting (x + 3) equal to 4.23083916 and -4.23083916.Subproblem 1
x + 3 = 4.23083916 Simplifying x + 3 = 4.23083916 Reorder the terms: 3 + x = 4.23083916 Solving 3 + x = 4.23083916 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 = 4.23083916 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.23083916 + -3 x = 4.23083916 + -3 Combine like terms: 4.23083916 + -3 = 1.23083916 x = 1.23083916 Simplifying x = 1.23083916Subproblem 2
x + 3 = -4.23083916 Simplifying x + 3 = -4.23083916 Reorder the terms: 3 + x = -4.23083916 Solving 3 + x = -4.23083916 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 = -4.23083916 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.23083916 + -3 x = -4.23083916 + -3 Combine like terms: -4.23083916 + -3 = -7.23083916 x = -7.23083916 Simplifying x = -7.23083916Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.23083916, -7.23083916}
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