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Simplifying 9x2 + -71x + 4 = 0 Reorder the terms: 4 + -71x + 9x2 = 0 Solving 4 + -71x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + -7.888888889x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -7.888888889x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -7.888888889x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -7.888888889x + x2 = 0 + -0.4444444444 -7.888888889x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -7.888888889x + x2 = -0.4444444444 The x term is -7.888888889x. Take half its coefficient (-3.944444445). Square it (15.55864198) and add it to both sides. Add '15.55864198' to each side of the equation. -7.888888889x + 15.55864198 + x2 = -0.4444444444 + 15.55864198 Reorder the terms: 15.55864198 + -7.888888889x + x2 = -0.4444444444 + 15.55864198 Combine like terms: -0.4444444444 + 15.55864198 = 15.1141975356 15.55864198 + -7.888888889x + x2 = 15.1141975356 Factor a perfect square on the left side: (x + -3.944444445)(x + -3.944444445) = 15.1141975356 Calculate the square root of the right side: 3.887698231 Break this problem into two subproblems by setting (x + -3.944444445) equal to 3.887698231 and -3.887698231.Subproblem 1
x + -3.944444445 = 3.887698231 Simplifying x + -3.944444445 = 3.887698231 Reorder the terms: -3.944444445 + x = 3.887698231 Solving -3.944444445 + x = 3.887698231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.944444445' to each side of the equation. -3.944444445 + 3.944444445 + x = 3.887698231 + 3.944444445 Combine like terms: -3.944444445 + 3.944444445 = 0.000000000 0.000000000 + x = 3.887698231 + 3.944444445 x = 3.887698231 + 3.944444445 Combine like terms: 3.887698231 + 3.944444445 = 7.832142676 x = 7.832142676 Simplifying x = 7.832142676Subproblem 2
x + -3.944444445 = -3.887698231 Simplifying x + -3.944444445 = -3.887698231 Reorder the terms: -3.944444445 + x = -3.887698231 Solving -3.944444445 + x = -3.887698231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.944444445' to each side of the equation. -3.944444445 + 3.944444445 + x = -3.887698231 + 3.944444445 Combine like terms: -3.944444445 + 3.944444445 = 0.000000000 0.000000000 + x = -3.887698231 + 3.944444445 x = -3.887698231 + 3.944444445 Combine like terms: -3.887698231 + 3.944444445 = 0.056746214 x = 0.056746214 Simplifying x = 0.056746214Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.832142676, 0.056746214}
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