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Simplifying 30x2 + -70x + 35 = 0 Reorder the terms: 35 + -70x + 30x2 = 0 Solving 35 + -70x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(7 + -14x + 6x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + -14x + 6x2)' equal to zero and attempt to solve: Simplifying 7 + -14x + 6x2 = 0 Solving 7 + -14x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + -2.333333333x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + -2.333333333x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + -2.333333333x + x2 = 0 + -1.166666667 -2.333333333x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 -2.333333333x + x2 = -1.166666667 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = -1.166666667 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = -1.166666667 + 1.361111112 Combine like terms: -1.166666667 + 1.361111112 = 0.194444445 1.361111112 + -2.333333333x + x2 = 0.194444445 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 0.194444445 Calculate the square root of the right side: 0.440958552 Break this problem into two subproblems by setting (x + -1.166666667) equal to 0.440958552 and -0.440958552.Subproblem 1
x + -1.166666667 = 0.440958552 Simplifying x + -1.166666667 = 0.440958552 Reorder the terms: -1.166666667 + x = 0.440958552 Solving -1.166666667 + x = 0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 0.440958552 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 0.440958552 + 1.166666667 x = 0.440958552 + 1.166666667 Combine like terms: 0.440958552 + 1.166666667 = 1.607625219 x = 1.607625219 Simplifying x = 1.607625219Subproblem 2
x + -1.166666667 = -0.440958552 Simplifying x + -1.166666667 = -0.440958552 Reorder the terms: -1.166666667 + x = -0.440958552 Solving -1.166666667 + x = -0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -0.440958552 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -0.440958552 + 1.166666667 x = -0.440958552 + 1.166666667 Combine like terms: -0.440958552 + 1.166666667 = 0.725708115 x = 0.725708115 Simplifying x = 0.725708115Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.607625219, 0.725708115}Solution
x = {1.607625219, 0.725708115}
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