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Simplifying -4.9x2 + -48x + 160 = 0 Reorder the terms: 160 + -48x + -4.9x2 = 0 Solving 160 + -48x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -32.65306122 + 9.795918367x + x2 = 0 Move the constant term to the right: Add '32.65306122' to each side of the equation. -32.65306122 + 9.795918367x + 32.65306122 + x2 = 0 + 32.65306122 Reorder the terms: -32.65306122 + 32.65306122 + 9.795918367x + x2 = 0 + 32.65306122 Combine like terms: -32.65306122 + 32.65306122 = 0.00000000 0.00000000 + 9.795918367x + x2 = 0 + 32.65306122 9.795918367x + x2 = 0 + 32.65306122 Combine like terms: 0 + 32.65306122 = 32.65306122 9.795918367x + x2 = 32.65306122 The x term is 9.795918367x. Take half its coefficient (4.897959184). Square it (23.99000417) and add it to both sides. Add '23.99000417' to each side of the equation. 9.795918367x + 23.99000417 + x2 = 32.65306122 + 23.99000417 Reorder the terms: 23.99000417 + 9.795918367x + x2 = 32.65306122 + 23.99000417 Combine like terms: 32.65306122 + 23.99000417 = 56.64306539 23.99000417 + 9.795918367x + x2 = 56.64306539 Factor a perfect square on the left side: (x + 4.897959184)(x + 4.897959184) = 56.64306539 Calculate the square root of the right side: 7.526158741 Break this problem into two subproblems by setting (x + 4.897959184) equal to 7.526158741 and -7.526158741.Subproblem 1
x + 4.897959184 = 7.526158741 Simplifying x + 4.897959184 = 7.526158741 Reorder the terms: 4.897959184 + x = 7.526158741 Solving 4.897959184 + x = 7.526158741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.897959184' to each side of the equation. 4.897959184 + -4.897959184 + x = 7.526158741 + -4.897959184 Combine like terms: 4.897959184 + -4.897959184 = 0.000000000 0.000000000 + x = 7.526158741 + -4.897959184 x = 7.526158741 + -4.897959184 Combine like terms: 7.526158741 + -4.897959184 = 2.628199557 x = 2.628199557 Simplifying x = 2.628199557Subproblem 2
x + 4.897959184 = -7.526158741 Simplifying x + 4.897959184 = -7.526158741 Reorder the terms: 4.897959184 + x = -7.526158741 Solving 4.897959184 + x = -7.526158741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.897959184' to each side of the equation. 4.897959184 + -4.897959184 + x = -7.526158741 + -4.897959184 Combine like terms: 4.897959184 + -4.897959184 = 0.000000000 0.000000000 + x = -7.526158741 + -4.897959184 x = -7.526158741 + -4.897959184 Combine like terms: -7.526158741 + -4.897959184 = -12.424117925 x = -12.424117925 Simplifying x = -12.424117925Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.628199557, -12.424117925}
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