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Simplifying 50x2 + 40x + -45 = 0 Reorder the terms: -45 + 40x + 50x2 = 0 Solving -45 + 40x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + 8x + 10x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + 8x + 10x2)' equal to zero and attempt to solve: Simplifying -9 + 8x + 10x2 = 0 Solving -9 + 8x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + 0.8x + x2 = 0.0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 0.8x + 0.9 + x2 = 0.0 + 0.9 Reorder the terms: -0.9 + 0.9 + 0.8x + x2 = 0.0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 0.8x + x2 = 0.0 + 0.9 0.8x + x2 = 0.0 + 0.9 Combine like terms: 0.0 + 0.9 = 0.9 0.8x + x2 = 0.9 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 = 0.9 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 0.9 + 0.16 Combine like terms: 0.9 + 0.16 = 1.06 0.16 + 0.8x + x2 = 1.06 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 1.06 Calculate the square root of the right side: 1.029563014 Break this problem into two subproblems by setting (x + 0.4) equal to 1.029563014 and -1.029563014.Subproblem 1
x + 0.4 = 1.029563014 Simplifying x + 0.4 = 1.029563014 Reorder the terms: 0.4 + x = 1.029563014 Solving 0.4 + x = 1.029563014 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 = 1.029563014 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.029563014 + -0.4 x = 1.029563014 + -0.4 Combine like terms: 1.029563014 + -0.4 = 0.629563014 x = 0.629563014 Simplifying x = 0.629563014Subproblem 2
x + 0.4 = -1.029563014 Simplifying x + 0.4 = -1.029563014 Reorder the terms: 0.4 + x = -1.029563014 Solving 0.4 + x = -1.029563014 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 = -1.029563014 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.029563014 + -0.4 x = -1.029563014 + -0.4 Combine like terms: -1.029563014 + -0.4 = -1.429563014 x = -1.429563014 Simplifying x = -1.429563014Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.629563014, -1.429563014}Solution
x = {0.629563014, -1.429563014}
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