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Simplifying 10x2 + 8x + 16 = 100 Reorder the terms: 16 + 8x + 10x2 = 100 Solving 16 + 8x + 10x2 = 100 Solving for variable 'x'. Reorder the terms: 16 + -100 + 8x + 10x2 = 100 + -100 Combine like terms: 16 + -100 = -84 -84 + 8x + 10x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -84 + 8x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + 4x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-42 + 4x + 5x2)' equal to zero and attempt to solve: Simplifying -42 + 4x + 5x2 = 0 Solving -42 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.4 + 0.8x + x2 = 0 Move the constant term to the right: Add '8.4' to each side of the equation. -8.4 + 0.8x + 8.4 + x2 = 0 + 8.4 Reorder the terms: -8.4 + 8.4 + 0.8x + x2 = 0 + 8.4 Combine like terms: -8.4 + 8.4 = 0.0 0.0 + 0.8x + x2 = 0 + 8.4 0.8x + x2 = 0 + 8.4 Combine like terms: 0 + 8.4 = 8.4 0.8x + x2 = 8.4 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 8.4 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 8.4 + 0.16 Combine like terms: 8.4 + 0.16 = 8.56 0.16 + 0.8x + x2 = 8.56 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 8.56 Calculate the square root of the right side: 2.925747768 Break this problem into two subproblems by setting (x + 0.4) equal to 2.925747768 and -2.925747768.Subproblem 1
x + 0.4 = 2.925747768 Simplifying x + 0.4 = 2.925747768 Reorder the terms: 0.4 + x = 2.925747768 Solving 0.4 + x = 2.925747768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 2.925747768 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.925747768 + -0.4 x = 2.925747768 + -0.4 Combine like terms: 2.925747768 + -0.4 = 2.525747768 x = 2.525747768 Simplifying x = 2.525747768Subproblem 2
x + 0.4 = -2.925747768 Simplifying x + 0.4 = -2.925747768 Reorder the terms: 0.4 + x = -2.925747768 Solving 0.4 + x = -2.925747768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -2.925747768 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.925747768 + -0.4 x = -2.925747768 + -0.4 Combine like terms: -2.925747768 + -0.4 = -3.325747768 x = -3.325747768 Simplifying x = -3.325747768Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.525747768, -3.325747768}Solution
x = {2.525747768, -3.325747768}
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