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Simplifying 136 = (7x + -4) * x Reorder the terms: 136 = (-4 + 7x) * x Reorder the terms for easier multiplication: 136 = x(-4 + 7x) 136 = (-4 * x + 7x * x) 136 = (-4x + 7x2) Solving 136 = -4x + 7x2 Solving for variable 'x'. Reorder the terms: 136 + 4x + -7x2 = -4x + 4x + 7x2 + -7x2 Combine like terms: -4x + 4x = 0 136 + 4x + -7x2 = 0 + 7x2 + -7x2 136 + 4x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 136 + 4x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -19.42857143 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '19.42857143' to each side of the equation. -19.42857143 + -0.5714285714x + 19.42857143 + x2 = 0 + 19.42857143 Reorder the terms: -19.42857143 + 19.42857143 + -0.5714285714x + x2 = 0 + 19.42857143 Combine like terms: -19.42857143 + 19.42857143 = 0.00000000 0.00000000 + -0.5714285714x + x2 = 0 + 19.42857143 -0.5714285714x + x2 = 0 + 19.42857143 Combine like terms: 0 + 19.42857143 = 19.42857143 -0.5714285714x + x2 = 19.42857143 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 = 19.42857143 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 19.42857143 + 0.08163265305 Combine like terms: 19.42857143 + 0.08163265305 = 19.51020408305 0.08163265305 + -0.5714285714x + x2 = 19.51020408305 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 19.51020408305 Calculate the square root of the right side: 4.417035667 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 4.417035667 and -4.417035667.Subproblem 1
x + -0.2857142857 = 4.417035667 Simplifying x + -0.2857142857 = 4.417035667 Reorder the terms: -0.2857142857 + x = 4.417035667 Solving -0.2857142857 + x = 4.417035667 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 = 4.417035667 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 4.417035667 + 0.2857142857 x = 4.417035667 + 0.2857142857 Combine like terms: 4.417035667 + 0.2857142857 = 4.7027499527 x = 4.7027499527 Simplifying x = 4.7027499527Subproblem 2
x + -0.2857142857 = -4.417035667 Simplifying x + -0.2857142857 = -4.417035667 Reorder the terms: -0.2857142857 + x = -4.417035667 Solving -0.2857142857 + x = -4.417035667 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 = -4.417035667 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -4.417035667 + 0.2857142857 x = -4.417035667 + 0.2857142857 Combine like terms: -4.417035667 + 0.2857142857 = -4.1313213813 x = -4.1313213813 Simplifying x = -4.1313213813Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.7027499527, -4.1313213813}
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