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Simplifying (6x + -1) * 7x = 90 Reorder the terms: (-1 + 6x) * 7x = 90 Reorder the terms for easier multiplication: 7x(-1 + 6x) = 90 (-1 * 7x + 6x * 7x) = 90 (-7x + 42x2) = 90 Solving -7x + 42x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -7x + 42x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -7x + 42x2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -2.142857143 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + -0.1666666667x + 2.142857143 + x2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + -0.1666666667x + x2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + -0.1666666667x + x2 = 0 + 2.142857143 -0.1666666667x + x2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 -0.1666666667x + x2 = 2.142857143 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 2.142857143 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 2.142857143 + 0.006944444447 Combine like terms: 2.142857143 + 0.006944444447 = 2.149801587447 0.006944444447 + -0.1666666667x + x2 = 2.149801587447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 2.149801587447 Calculate the square root of the right side: 1.46622017 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 1.46622017 and -1.46622017.Subproblem 1
x + -0.08333333335 = 1.46622017 Simplifying x + -0.08333333335 = 1.46622017 Reorder the terms: -0.08333333335 + x = 1.46622017 Solving -0.08333333335 + x = 1.46622017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 1.46622017 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 1.46622017 + 0.08333333335 x = 1.46622017 + 0.08333333335 Combine like terms: 1.46622017 + 0.08333333335 = 1.54955350335 x = 1.54955350335 Simplifying x = 1.54955350335Subproblem 2
x + -0.08333333335 = -1.46622017 Simplifying x + -0.08333333335 = -1.46622017 Reorder the terms: -0.08333333335 + x = -1.46622017 Solving -0.08333333335 + x = -1.46622017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -1.46622017 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -1.46622017 + 0.08333333335 x = -1.46622017 + 0.08333333335 Combine like terms: -1.46622017 + 0.08333333335 = -1.38288683665 x = -1.38288683665 Simplifying x = -1.38288683665Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.54955350335, -1.38288683665}
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