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Simplifying 426x2 + -645x + 243 = 0 Reorder the terms: 243 + -645x + 426x2 = 0 Solving 243 + -645x + 426x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(81 + -215x + 142x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(81 + -215x + 142x2)' equal to zero and attempt to solve: Simplifying 81 + -215x + 142x2 = 0 Solving 81 + -215x + 142x2 = 0 Begin completing the square. Divide all terms by 142 the coefficient of the squared term: Divide each side by '142'. 0.5704225352 + -1.514084507x + x2 = 0 Move the constant term to the right: Add '-0.5704225352' to each side of the equation. 0.5704225352 + -1.514084507x + -0.5704225352 + x2 = 0 + -0.5704225352 Reorder the terms: 0.5704225352 + -0.5704225352 + -1.514084507x + x2 = 0 + -0.5704225352 Combine like terms: 0.5704225352 + -0.5704225352 = 0.0000000000 0.0000000000 + -1.514084507x + x2 = 0 + -0.5704225352 -1.514084507x + x2 = 0 + -0.5704225352 Combine like terms: 0 + -0.5704225352 = -0.5704225352 -1.514084507x + x2 = -0.5704225352 The x term is -1.514084507x. Take half its coefficient (-0.7570422535). Square it (0.5731129736) and add it to both sides. Add '0.5731129736' to each side of the equation. -1.514084507x + 0.5731129736 + x2 = -0.5704225352 + 0.5731129736 Reorder the terms: 0.5731129736 + -1.514084507x + x2 = -0.5704225352 + 0.5731129736 Combine like terms: -0.5704225352 + 0.5731129736 = 0.0026904384 0.5731129736 + -1.514084507x + x2 = 0.0026904384 Factor a perfect square on the left side: (x + -0.7570422535)(x + -0.7570422535) = 0.0026904384 Calculate the square root of the right side: 0.051869436 Break this problem into two subproblems by setting (x + -0.7570422535) equal to 0.051869436 and -0.051869436.Subproblem 1
x + -0.7570422535 = 0.051869436 Simplifying x + -0.7570422535 = 0.051869436 Reorder the terms: -0.7570422535 + x = 0.051869436 Solving -0.7570422535 + x = 0.051869436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7570422535' to each side of the equation. -0.7570422535 + 0.7570422535 + x = 0.051869436 + 0.7570422535 Combine like terms: -0.7570422535 + 0.7570422535 = 0.0000000000 0.0000000000 + x = 0.051869436 + 0.7570422535 x = 0.051869436 + 0.7570422535 Combine like terms: 0.051869436 + 0.7570422535 = 0.8089116895 x = 0.8089116895 Simplifying x = 0.8089116895Subproblem 2
x + -0.7570422535 = -0.051869436 Simplifying x + -0.7570422535 = -0.051869436 Reorder the terms: -0.7570422535 + x = -0.051869436 Solving -0.7570422535 + x = -0.051869436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7570422535' to each side of the equation. -0.7570422535 + 0.7570422535 + x = -0.051869436 + 0.7570422535 Combine like terms: -0.7570422535 + 0.7570422535 = 0.0000000000 0.0000000000 + x = -0.051869436 + 0.7570422535 x = -0.051869436 + 0.7570422535 Combine like terms: -0.051869436 + 0.7570422535 = 0.7051728175 x = 0.7051728175 Simplifying x = 0.7051728175Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8089116895, 0.7051728175}Solution
x = {0.8089116895, 0.7051728175}
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