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Simplifying 10x2 + -98x + 32 = 0 Reorder the terms: 32 + -98x + 10x2 = 0 Solving 32 + -98x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -49x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + -49x + 5x2)' equal to zero and attempt to solve: Simplifying 16 + -49x + 5x2 = 0 Solving 16 + -49x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + -9.8x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -9.8x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -9.8x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -9.8x + x2 = 0 + -3.2 -9.8x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -9.8x + x2 = -3.2 The x term is -9.8x. Take half its coefficient (-4.9). Square it (24.01) and add it to both sides. Add '24.01' to each side of the equation. -9.8x + 24.01 + x2 = -3.2 + 24.01 Reorder the terms: 24.01 + -9.8x + x2 = -3.2 + 24.01 Combine like terms: -3.2 + 24.01 = 20.81 24.01 + -9.8x + x2 = 20.81 Factor a perfect square on the left side: (x + -4.9)(x + -4.9) = 20.81 Calculate the square root of the right side: 4.561797891 Break this problem into two subproblems by setting (x + -4.9) equal to 4.561797891 and -4.561797891.Subproblem 1
x + -4.9 = 4.561797891 Simplifying x + -4.9 = 4.561797891 Reorder the terms: -4.9 + x = 4.561797891 Solving -4.9 + x = 4.561797891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.9' to each side of the equation. -4.9 + 4.9 + x = 4.561797891 + 4.9 Combine like terms: -4.9 + 4.9 = 0.0 0.0 + x = 4.561797891 + 4.9 x = 4.561797891 + 4.9 Combine like terms: 4.561797891 + 4.9 = 9.461797891 x = 9.461797891 Simplifying x = 9.461797891Subproblem 2
x + -4.9 = -4.561797891 Simplifying x + -4.9 = -4.561797891 Reorder the terms: -4.9 + x = -4.561797891 Solving -4.9 + x = -4.561797891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.9' to each side of the equation. -4.9 + 4.9 + x = -4.561797891 + 4.9 Combine like terms: -4.9 + 4.9 = 0.0 0.0 + x = -4.561797891 + 4.9 x = -4.561797891 + 4.9 Combine like terms: -4.561797891 + 4.9 = 0.338202109 x = 0.338202109 Simplifying x = 0.338202109Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.461797891, 0.338202109}Solution
x = {9.461797891, 0.338202109}
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