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Simplifying 26x2 + -7.2x + 0.26 = 0 Reorder the terms: 0.26 + -7.2x + 26x2 = 0 Solving 0.26 + -7.2x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. 0.01 + -0.2769230769x + x2 = 0 Move the constant term to the right: Add '-0.01' to each side of the equation. 0.01 + -0.2769230769x + -0.01 + x2 = 0 + -0.01 Reorder the terms: 0.01 + -0.01 + -0.2769230769x + x2 = 0 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + -0.2769230769x + x2 = 0 + -0.01 -0.2769230769x + x2 = 0 + -0.01 Combine like terms: 0 + -0.01 = -0.01 -0.2769230769x + x2 = -0.01 The x term is -0.2769230769x. Take half its coefficient (-0.1384615385). Square it (0.01917159764) and add it to both sides. Add '0.01917159764' to each side of the equation. -0.2769230769x + 0.01917159764 + x2 = -0.01 + 0.01917159764 Reorder the terms: 0.01917159764 + -0.2769230769x + x2 = -0.01 + 0.01917159764 Combine like terms: -0.01 + 0.01917159764 = 0.00917159764 0.01917159764 + -0.2769230769x + x2 = 0.00917159764 Factor a perfect square on the left side: (x + -0.1384615385)(x + -0.1384615385) = 0.00917159764 Calculate the square root of the right side: 0.095768458 Break this problem into two subproblems by setting (x + -0.1384615385) equal to 0.095768458 and -0.095768458.Subproblem 1
x + -0.1384615385 = 0.095768458 Simplifying x + -0.1384615385 = 0.095768458 Reorder the terms: -0.1384615385 + x = 0.095768458 Solving -0.1384615385 + x = 0.095768458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1384615385' to each side of the equation. -0.1384615385 + 0.1384615385 + x = 0.095768458 + 0.1384615385 Combine like terms: -0.1384615385 + 0.1384615385 = 0.0000000000 0.0000000000 + x = 0.095768458 + 0.1384615385 x = 0.095768458 + 0.1384615385 Combine like terms: 0.095768458 + 0.1384615385 = 0.2342299965 x = 0.2342299965 Simplifying x = 0.2342299965Subproblem 2
x + -0.1384615385 = -0.095768458 Simplifying x + -0.1384615385 = -0.095768458 Reorder the terms: -0.1384615385 + x = -0.095768458 Solving -0.1384615385 + x = -0.095768458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1384615385' to each side of the equation. -0.1384615385 + 0.1384615385 + x = -0.095768458 + 0.1384615385 Combine like terms: -0.1384615385 + 0.1384615385 = 0.0000000000 0.0000000000 + x = -0.095768458 + 0.1384615385 x = -0.095768458 + 0.1384615385 Combine like terms: -0.095768458 + 0.1384615385 = 0.0426930805 x = 0.0426930805 Simplifying x = 0.0426930805Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2342299965, 0.0426930805}
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