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Simplifying -7 = 7.37802(x) + (-4.9)(x2) Solving -7 = 7.37802x + -4.9x2 Solving for variable 'x'. Reorder the terms: -7 + -7.37802x + 4.9x2 = 7.37802x + -7.37802x + -4.9x2 + 4.9x2 Combine like terms: 7.37802x + -7.37802x = 0.00000 -7 + -7.37802x + 4.9x2 = 0.00000 + -4.9x2 + 4.9x2 -7 + -7.37802x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -7 + -7.37802x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.428571429 + -1.505718367x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -1.505718367x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -1.505718367x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -1.505718367x + x2 = 0 + 1.428571429 -1.505718367x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -1.505718367x + x2 = 1.428571429 The x term is -1.505718367x. Take half its coefficient (-0.7528591835). Square it (0.5667969502) and add it to both sides. Add '0.5667969502' to each side of the equation. -1.505718367x + 0.5667969502 + x2 = 1.428571429 + 0.5667969502 Reorder the terms: 0.5667969502 + -1.505718367x + x2 = 1.428571429 + 0.5667969502 Combine like terms: 1.428571429 + 0.5667969502 = 1.9953683792 0.5667969502 + -1.505718367x + x2 = 1.9953683792 Factor a perfect square on the left side: (x + -0.7528591835)(x + -0.7528591835) = 1.9953683792 Calculate the square root of the right side: 1.412575088 Break this problem into two subproblems by setting (x + -0.7528591835) equal to 1.412575088 and -1.412575088.Subproblem 1
x + -0.7528591835 = 1.412575088 Simplifying x + -0.7528591835 = 1.412575088 Reorder the terms: -0.7528591835 + x = 1.412575088 Solving -0.7528591835 + x = 1.412575088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7528591835' to each side of the equation. -0.7528591835 + 0.7528591835 + x = 1.412575088 + 0.7528591835 Combine like terms: -0.7528591835 + 0.7528591835 = 0.0000000000 0.0000000000 + x = 1.412575088 + 0.7528591835 x = 1.412575088 + 0.7528591835 Combine like terms: 1.412575088 + 0.7528591835 = 2.1654342715 x = 2.1654342715 Simplifying x = 2.1654342715Subproblem 2
x + -0.7528591835 = -1.412575088 Simplifying x + -0.7528591835 = -1.412575088 Reorder the terms: -0.7528591835 + x = -1.412575088 Solving -0.7528591835 + x = -1.412575088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7528591835' to each side of the equation. -0.7528591835 + 0.7528591835 + x = -1.412575088 + 0.7528591835 Combine like terms: -0.7528591835 + 0.7528591835 = 0.0000000000 0.0000000000 + x = -1.412575088 + 0.7528591835 x = -1.412575088 + 0.7528591835 Combine like terms: -1.412575088 + 0.7528591835 = -0.6597159045 x = -0.6597159045 Simplifying x = -0.6597159045Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1654342715, -0.6597159045}
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