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Simplifying -35x2 + 75x + 50 = 0 Reorder the terms: 50 + 75x + -35x2 = 0 Solving 50 + 75x + -35x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(10 + 15x + -7x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + 15x + -7x2)' equal to zero and attempt to solve: Simplifying 10 + 15x + -7x2 = 0 Solving 10 + 15x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.428571429 + -2.142857143x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -2.142857143x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -2.142857143x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -2.142857143x + x2 = 0 + 1.428571429 -2.142857143x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -2.142857143x + x2 = 1.428571429 The x term is -2.142857143x. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143x + 1.147959185 + x2 = 1.428571429 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143x + x2 = 1.428571429 + 1.147959185 Combine like terms: 1.428571429 + 1.147959185 = 2.576530614 1.147959185 + -2.142857143x + x2 = 2.576530614 Factor a perfect square on the left side: (x + -1.071428572)(x + -1.071428572) = 2.576530614 Calculate the square root of the right side: 1.605157504 Break this problem into two subproblems by setting (x + -1.071428572) equal to 1.605157504 and -1.605157504.Subproblem 1
x + -1.071428572 = 1.605157504 Simplifying x + -1.071428572 = 1.605157504 Reorder the terms: -1.071428572 + x = 1.605157504 Solving -1.071428572 + x = 1.605157504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = 1.605157504 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = 1.605157504 + 1.071428572 x = 1.605157504 + 1.071428572 Combine like terms: 1.605157504 + 1.071428572 = 2.676586076 x = 2.676586076 Simplifying x = 2.676586076Subproblem 2
x + -1.071428572 = -1.605157504 Simplifying x + -1.071428572 = -1.605157504 Reorder the terms: -1.071428572 + x = -1.605157504 Solving -1.071428572 + x = -1.605157504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = -1.605157504 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = -1.605157504 + 1.071428572 x = -1.605157504 + 1.071428572 Combine like terms: -1.605157504 + 1.071428572 = -0.533728932 x = -0.533728932 Simplifying x = -0.533728932Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.676586076, -0.533728932}Solution
x = {2.676586076, -0.533728932}
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