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Simplifying 10x2 + 6x + -99 = 0 Reorder the terms: -99 + 6x + 10x2 = 0 Solving -99 + 6x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -9.9 + 0.6x + x2 = 0 Move the constant term to the right: Add '9.9' to each side of the equation. -9.9 + 0.6x + 9.9 + x2 = 0 + 9.9 Reorder the terms: -9.9 + 9.9 + 0.6x + x2 = 0 + 9.9 Combine like terms: -9.9 + 9.9 = 0.0 0.0 + 0.6x + x2 = 0 + 9.9 0.6x + x2 = 0 + 9.9 Combine like terms: 0 + 9.9 = 9.9 0.6x + x2 = 9.9 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 9.9 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 9.9 + 0.09 Combine like terms: 9.9 + 0.09 = 9.99 0.09 + 0.6x + x2 = 9.99 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 9.99 Calculate the square root of the right side: 3.160696126 Break this problem into two subproblems by setting (x + 0.3) equal to 3.160696126 and -3.160696126.Subproblem 1
x + 0.3 = 3.160696126 Simplifying x + 0.3 = 3.160696126 Reorder the terms: 0.3 + x = 3.160696126 Solving 0.3 + x = 3.160696126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 3.160696126 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 3.160696126 + -0.3 x = 3.160696126 + -0.3 Combine like terms: 3.160696126 + -0.3 = 2.860696126 x = 2.860696126 Simplifying x = 2.860696126Subproblem 2
x + 0.3 = -3.160696126 Simplifying x + 0.3 = -3.160696126 Reorder the terms: 0.3 + x = -3.160696126 Solving 0.3 + x = -3.160696126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -3.160696126 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -3.160696126 + -0.3 x = -3.160696126 + -0.3 Combine like terms: -3.160696126 + -0.3 = -3.460696126 x = -3.460696126 Simplifying x = -3.460696126Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.860696126, -3.460696126}
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