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Simplifying 7(6x2 + -1x) = 55 Reorder the terms: 7(-1x + 6x2) = 55 (-1x * 7 + 6x2 * 7) = 55 (-7x + 42x2) = 55 Solving -7x + 42x2 = 55 Solving for variable 'x'. Reorder the terms: -55 + -7x + 42x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + -7x + 42x2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -1.30952381 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '1.30952381' to each side of the equation. -1.30952381 + -0.1666666667x + 1.30952381 + x2 = 0 + 1.30952381 Reorder the terms: -1.30952381 + 1.30952381 + -0.1666666667x + x2 = 0 + 1.30952381 Combine like terms: -1.30952381 + 1.30952381 = 0.00000000 0.00000000 + -0.1666666667x + x2 = 0 + 1.30952381 -0.1666666667x + x2 = 0 + 1.30952381 Combine like terms: 0 + 1.30952381 = 1.30952381 -0.1666666667x + x2 = 1.30952381 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 = 1.30952381 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 1.30952381 + 0.006944444447 Combine like terms: 1.30952381 + 0.006944444447 = 1.316468254447 0.006944444447 + -0.1666666667x + x2 = 1.316468254447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 1.316468254447 Calculate the square root of the right side: 1.147374505 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 1.147374505 and -1.147374505.Subproblem 1
x + -0.08333333335 = 1.147374505 Simplifying x + -0.08333333335 = 1.147374505 Reorder the terms: -0.08333333335 + x = 1.147374505 Solving -0.08333333335 + x = 1.147374505 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 = 1.147374505 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 1.147374505 + 0.08333333335 x = 1.147374505 + 0.08333333335 Combine like terms: 1.147374505 + 0.08333333335 = 1.23070783835 x = 1.23070783835 Simplifying x = 1.23070783835Subproblem 2
x + -0.08333333335 = -1.147374505 Simplifying x + -0.08333333335 = -1.147374505 Reorder the terms: -0.08333333335 + x = -1.147374505 Solving -0.08333333335 + x = -1.147374505 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 = -1.147374505 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -1.147374505 + 0.08333333335 x = -1.147374505 + 0.08333333335 Combine like terms: -1.147374505 + 0.08333333335 = -1.06404117165 x = -1.06404117165 Simplifying x = -1.06404117165Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.23070783835, -1.06404117165}
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