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Simplifying 0 = -4.9x2 + 7x + 0.6 Reorder the terms: 0 = 0.6 + 7x + -4.9x2 Solving 0 = 0.6 + 7x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -0.6 = -0.6 -0.6 + -7x + 4.9x2 = 0.6 + 7x + -4.9x2 + -0.6 + -7x + 4.9x2 Reorder the terms: -0.6 + -7x + 4.9x2 = 0.6 + -0.6 + 7x + -7x + -4.9x2 + 4.9x2 Combine like terms: 0.6 + -0.6 = 0.0 -0.6 + -7x + 4.9x2 = 0.0 + 7x + -7x + -4.9x2 + 4.9x2 -0.6 + -7x + 4.9x2 = 7x + -7x + -4.9x2 + 4.9x2 Combine like terms: 7x + -7x = 0 -0.6 + -7x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -0.6 + -7x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -0.6 + -7x + 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'. -0.1224489796 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '0.1224489796' to each side of the equation. -0.1224489796 + -1.428571429x + 0.1224489796 + x2 = 0 + 0.1224489796 Reorder the terms: -0.1224489796 + 0.1224489796 + -1.428571429x + x2 = 0 + 0.1224489796 Combine like terms: -0.1224489796 + 0.1224489796 = 0.0000000000 0.0000000000 + -1.428571429x + x2 = 0 + 0.1224489796 -1.428571429x + x2 = 0 + 0.1224489796 Combine like terms: 0 + 0.1224489796 = 0.1224489796 -1.428571429x + x2 = 0.1224489796 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 0.1224489796 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 0.1224489796 + 0.5102040819 Combine like terms: 0.1224489796 + 0.5102040819 = 0.6326530615 0.5102040819 + -1.428571429x + x2 = 0.6326530615 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 0.6326530615 Calculate the square root of the right side: 0.795394909 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 0.795394909 and -0.795394909.Subproblem 1
x + -0.7142857145 = 0.795394909 Simplifying x + -0.7142857145 = 0.795394909 Reorder the terms: -0.7142857145 + x = 0.795394909 Solving -0.7142857145 + x = 0.795394909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 0.795394909 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 0.795394909 + 0.7142857145 x = 0.795394909 + 0.7142857145 Combine like terms: 0.795394909 + 0.7142857145 = 1.5096806235 x = 1.5096806235 Simplifying x = 1.5096806235Subproblem 2
x + -0.7142857145 = -0.795394909 Simplifying x + -0.7142857145 = -0.795394909 Reorder the terms: -0.7142857145 + x = -0.795394909 Solving -0.7142857145 + x = -0.795394909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -0.795394909 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -0.795394909 + 0.7142857145 x = -0.795394909 + 0.7142857145 Combine like terms: -0.795394909 + 0.7142857145 = -0.0811091945 x = -0.0811091945 Simplifying x = -0.0811091945Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5096806235, -0.0811091945}
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