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Simplifying 10x2 + -44x + 30 = 0 Reorder the terms: 30 + -44x + 10x2 = 0 Solving 30 + -44x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -22x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -22x + 5x2)' equal to zero and attempt to solve: Simplifying 15 + -22x + 5x2 = 0 Solving 15 + -22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + -4.4x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.4x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -4.4x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.4x + x2 = 0 + -3 -4.4x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.4x + x2 = -3 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = -3 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = -3 + 4.84 Combine like terms: -3 + 4.84 = 1.84 4.84 + -4.4x + x2 = 1.84 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x + -2.2) equal to 1.356465997 and -1.356465997.Subproblem 1
x + -2.2 = 1.356465997 Simplifying x + -2.2 = 1.356465997 Reorder the terms: -2.2 + x = 1.356465997 Solving -2.2 + x = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 1.356465997 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 1.356465997 + 2.2 x = 1.356465997 + 2.2 Combine like terms: 1.356465997 + 2.2 = 3.556465997 x = 3.556465997 Simplifying x = 3.556465997Subproblem 2
x + -2.2 = -1.356465997 Simplifying x + -2.2 = -1.356465997 Reorder the terms: -2.2 + x = -1.356465997 Solving -2.2 + x = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -1.356465997 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -1.356465997 + 2.2 x = -1.356465997 + 2.2 Combine like terms: -1.356465997 + 2.2 = 0.843534003 x = 0.843534003 Simplifying x = 0.843534003Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.556465997, 0.843534003}Solution
x = {3.556465997, 0.843534003}
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