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Simplifying 70 = 42x + 4x2 Solving 70 = 42x + 4x2 Solving for variable 'x'. Reorder the terms: 70 + -42x + -4x2 = 42x + -42x + 4x2 + -4x2 Combine like terms: 42x + -42x = 0 70 + -42x + -4x2 = 0 + 4x2 + -4x2 70 + -42x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 70 + -42x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(35 + -21x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + -21x + -2x2)' equal to zero and attempt to solve: Simplifying 35 + -21x + -2x2 = 0 Solving 35 + -21x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -17.5 + 10.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 10.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 10.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 10.5x + x2 = 0 + 17.5 10.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 10.5x + x2 = 17.5 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 17.5 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 17.5 + 27.5625 Combine like terms: 17.5 + 27.5625 = 45.0625 27.5625 + 10.5x + x2 = 45.0625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 45.0625 Calculate the square root of the right side: 6.712860791 Break this problem into two subproblems by setting (x + 5.25) equal to 6.712860791 and -6.712860791.Subproblem 1
x + 5.25 = 6.712860791 Simplifying x + 5.25 = 6.712860791 Reorder the terms: 5.25 + x = 6.712860791 Solving 5.25 + x = 6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 6.712860791 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 6.712860791 + -5.25 x = 6.712860791 + -5.25 Combine like terms: 6.712860791 + -5.25 = 1.462860791 x = 1.462860791 Simplifying x = 1.462860791Subproblem 2
x + 5.25 = -6.712860791 Simplifying x + 5.25 = -6.712860791 Reorder the terms: 5.25 + x = -6.712860791 Solving 5.25 + x = -6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -6.712860791 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -6.712860791 + -5.25 x = -6.712860791 + -5.25 Combine like terms: -6.712860791 + -5.25 = -11.962860791 x = -11.962860791 Simplifying x = -11.962860791Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.462860791, -11.962860791}Solution
x = {1.462860791, -11.962860791}
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