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Simplifying -4.9x2 + 1.5x = -0.184 Reorder the terms: 1.5x + -4.9x2 = -0.184 Solving 1.5x + -4.9x2 = -0.184 Solving for variable 'x'. Reorder the terms: 0.184 + 1.5x + -4.9x2 = -0.184 + 0.184 Combine like terms: -0.184 + 0.184 = 0.000 0.184 + 1.5x + -4.9x2 = 0.000 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.03755102041 + -0.306122449x + x2 = 0.00 Move the constant term to the right: Add '0.03755102041' to each side of the equation. -0.03755102041 + -0.306122449x + 0.03755102041 + x2 = 0.00 + 0.03755102041 Reorder the terms: -0.03755102041 + 0.03755102041 + -0.306122449x + x2 = 0.00 + 0.03755102041 Combine like terms: -0.03755102041 + 0.03755102041 = 0.00000000000 0.00000000000 + -0.306122449x + x2 = 0.00 + 0.03755102041 -0.306122449x + x2 = 0.00 + 0.03755102041 Combine like terms: 0.00 + 0.03755102041 = 0.03755102041 -0.306122449x + x2 = 0.03755102041 The x term is -0.306122449x. Take half its coefficient (-0.1530612245). Square it (0.02342773845) and add it to both sides. Add '0.02342773845' to each side of the equation. -0.306122449x + 0.02342773845 + x2 = 0.03755102041 + 0.02342773845 Reorder the terms: 0.02342773845 + -0.306122449x + x2 = 0.03755102041 + 0.02342773845 Combine like terms: 0.03755102041 + 0.02342773845 = 0.06097875886 0.02342773845 + -0.306122449x + x2 = 0.06097875886 Factor a perfect square on the left side: (x + -0.1530612245)(x + -0.1530612245) = 0.06097875886 Calculate the square root of the right side: 0.246938776 Break this problem into two subproblems by setting (x + -0.1530612245) equal to 0.246938776 and -0.246938776.Subproblem 1
x + -0.1530612245 = 0.246938776 Simplifying x + -0.1530612245 = 0.246938776 Reorder the terms: -0.1530612245 + x = 0.246938776 Solving -0.1530612245 + x = 0.246938776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1530612245' to each side of the equation. -0.1530612245 + 0.1530612245 + x = 0.246938776 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + x = 0.246938776 + 0.1530612245 x = 0.246938776 + 0.1530612245 Combine like terms: 0.246938776 + 0.1530612245 = 0.4000000005 x = 0.4000000005 Simplifying x = 0.4000000005Subproblem 2
x + -0.1530612245 = -0.246938776 Simplifying x + -0.1530612245 = -0.246938776 Reorder the terms: -0.1530612245 + x = -0.246938776 Solving -0.1530612245 + x = -0.246938776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1530612245' to each side of the equation. -0.1530612245 + 0.1530612245 + x = -0.246938776 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + x = -0.246938776 + 0.1530612245 x = -0.246938776 + 0.1530612245 Combine like terms: -0.246938776 + 0.1530612245 = -0.0938775515 x = -0.0938775515 Simplifying x = -0.0938775515Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4000000005, -0.0938775515}
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