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Simplifying 7.54x + 2x2 = 100 Solving 7.54x + 2x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 7.54x + 2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 7.54x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50 + 3.77x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 3.77x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 3.77x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 3.77x + x2 = 0 + 50 3.77x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 3.77x + x2 = 50 The x term is 3.77x. Take half its coefficient (1.885). Square it (3.553225) and add it to both sides. Add '3.553225' to each side of the equation. 3.77x + 3.553225 + x2 = 50 + 3.553225 Reorder the terms: 3.553225 + 3.77x + x2 = 50 + 3.553225 Combine like terms: 50 + 3.553225 = 53.553225 3.553225 + 3.77x + x2 = 53.553225 Factor a perfect square on the left side: (x + 1.885)(x + 1.885) = 53.553225 Calculate the square root of the right side: 7.318006901 Break this problem into two subproblems by setting (x + 1.885) equal to 7.318006901 and -7.318006901.Subproblem 1
x + 1.885 = 7.318006901 Simplifying x + 1.885 = 7.318006901 Reorder the terms: 1.885 + x = 7.318006901 Solving 1.885 + x = 7.318006901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.885' to each side of the equation. 1.885 + -1.885 + x = 7.318006901 + -1.885 Combine like terms: 1.885 + -1.885 = 0.000 0.000 + x = 7.318006901 + -1.885 x = 7.318006901 + -1.885 Combine like terms: 7.318006901 + -1.885 = 5.433006901 x = 5.433006901 Simplifying x = 5.433006901Subproblem 2
x + 1.885 = -7.318006901 Simplifying x + 1.885 = -7.318006901 Reorder the terms: 1.885 + x = -7.318006901 Solving 1.885 + x = -7.318006901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.885' to each side of the equation. 1.885 + -1.885 + x = -7.318006901 + -1.885 Combine like terms: 1.885 + -1.885 = 0.000 0.000 + x = -7.318006901 + -1.885 x = -7.318006901 + -1.885 Combine like terms: -7.318006901 + -1.885 = -9.203006901 x = -9.203006901 Simplifying x = -9.203006901Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.433006901, -9.203006901}
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