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Simplifying 10x2 + 6x + -99 = 100 Reorder the terms: -99 + 6x + 10x2 = 100 Solving -99 + 6x + 10x2 = 100 Solving for variable 'x'. Reorder the terms: -99 + -100 + 6x + 10x2 = 100 + -100 Combine like terms: -99 + -100 = -199 -199 + 6x + 10x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -199 + 6x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -19.9 + 0.6x + x2 = 0 Move the constant term to the right: Add '19.9' to each side of the equation. -19.9 + 0.6x + 19.9 + x2 = 0 + 19.9 Reorder the terms: -19.9 + 19.9 + 0.6x + x2 = 0 + 19.9 Combine like terms: -19.9 + 19.9 = 0.0 0.0 + 0.6x + x2 = 0 + 19.9 0.6x + x2 = 0 + 19.9 Combine like terms: 0 + 19.9 = 19.9 0.6x + x2 = 19.9 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 = 19.9 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 19.9 + 0.09 Combine like terms: 19.9 + 0.09 = 19.99 0.09 + 0.6x + x2 = 19.99 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 19.99 Calculate the square root of the right side: 4.471017781 Break this problem into two subproblems by setting (x + 0.3) equal to 4.471017781 and -4.471017781.Subproblem 1
x + 0.3 = 4.471017781 Simplifying x + 0.3 = 4.471017781 Reorder the terms: 0.3 + x = 4.471017781 Solving 0.3 + x = 4.471017781 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 = 4.471017781 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 4.471017781 + -0.3 x = 4.471017781 + -0.3 Combine like terms: 4.471017781 + -0.3 = 4.171017781 x = 4.171017781 Simplifying x = 4.171017781Subproblem 2
x + 0.3 = -4.471017781 Simplifying x + 0.3 = -4.471017781 Reorder the terms: 0.3 + x = -4.471017781 Solving 0.3 + x = -4.471017781 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 = -4.471017781 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -4.471017781 + -0.3 x = -4.471017781 + -0.3 Combine like terms: -4.471017781 + -0.3 = -4.771017781 x = -4.771017781 Simplifying x = -4.771017781Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.171017781, -4.771017781}
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