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Simplifying 40 = (7x + -4)(3x) Reorder the terms: 40 = (-4 + 7x)(3x) Remove parenthesis around (3x) 40 = (-4 + 7x) * 3x Reorder the terms for easier multiplication: 40 = 3x(-4 + 7x) 40 = (-4 * 3x + 7x * 3x) 40 = (-12x + 21x2) Solving 40 = -12x + 21x2 Solving for variable 'x'. Reorder the terms: 40 + 12x + -21x2 = -12x + 12x + 21x2 + -21x2 Combine like terms: -12x + 12x = 0 40 + 12x + -21x2 = 0 + 21x2 + -21x2 40 + 12x + -21x2 = 21x2 + -21x2 Combine like terms: 21x2 + -21x2 = 0 40 + 12x + -21x2 = 0 Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -1.904761905 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '1.904761905' to each side of the equation. -1.904761905 + -0.5714285714x + 1.904761905 + x2 = 0 + 1.904761905 Reorder the terms: -1.904761905 + 1.904761905 + -0.5714285714x + x2 = 0 + 1.904761905 Combine like terms: -1.904761905 + 1.904761905 = 0.000000000 0.000000000 + -0.5714285714x + x2 = 0 + 1.904761905 -0.5714285714x + x2 = 0 + 1.904761905 Combine like terms: 0 + 1.904761905 = 1.904761905 -0.5714285714x + x2 = 1.904761905 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 1.904761905 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 1.904761905 + 0.08163265305 Combine like terms: 1.904761905 + 0.08163265305 = 1.98639455805 0.08163265305 + -0.5714285714x + x2 = 1.98639455805 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 1.98639455805 Calculate the square root of the right side: 1.409395104 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 1.409395104 and -1.409395104.Subproblem 1
x + -0.2857142857 = 1.409395104 Simplifying x + -0.2857142857 = 1.409395104 Reorder the terms: -0.2857142857 + x = 1.409395104 Solving -0.2857142857 + x = 1.409395104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 1.409395104 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 1.409395104 + 0.2857142857 x = 1.409395104 + 0.2857142857 Combine like terms: 1.409395104 + 0.2857142857 = 1.6951093897 x = 1.6951093897 Simplifying x = 1.6951093897Subproblem 2
x + -0.2857142857 = -1.409395104 Simplifying x + -0.2857142857 = -1.409395104 Reorder the terms: -0.2857142857 + x = -1.409395104 Solving -0.2857142857 + x = -1.409395104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -1.409395104 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -1.409395104 + 0.2857142857 x = -1.409395104 + 0.2857142857 Combine like terms: -1.409395104 + 0.2857142857 = -1.1236808183 x = -1.1236808183 Simplifying x = -1.1236808183Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6951093897, -1.1236808183}
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