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Simplifying 4.7X2 + 0.3X + -0.8 = 0 Reorder the terms: -0.8 + 0.3X + 4.7X2 = 0 Solving -0.8 + 0.3X + 4.7X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 4.7 the coefficient of the squared term: Divide each side by '4.7'. -0.170212766 + 0.06382978723X + X2 = 0 Move the constant term to the right: Add '0.170212766' to each side of the equation. -0.170212766 + 0.06382978723X + 0.170212766 + X2 = 0 + 0.170212766 Reorder the terms: -0.170212766 + 0.170212766 + 0.06382978723X + X2 = 0 + 0.170212766 Combine like terms: -0.170212766 + 0.170212766 = 0.000000000 0.000000000 + 0.06382978723X + X2 = 0 + 0.170212766 0.06382978723X + X2 = 0 + 0.170212766 Combine like terms: 0 + 0.170212766 = 0.170212766 0.06382978723X + X2 = 0.170212766 The X term is 0.06382978723X. Take half its coefficient (0.03191489362). Square it (0.001018560435) and add it to both sides. Add '0.001018560435' to each side of the equation. 0.06382978723X + 0.001018560435 + X2 = 0.170212766 + 0.001018560435 Reorder the terms: 0.001018560435 + 0.06382978723X + X2 = 0.170212766 + 0.001018560435 Combine like terms: 0.170212766 + 0.001018560435 = 0.171231326435 0.001018560435 + 0.06382978723X + X2 = 0.171231326435 Factor a perfect square on the left side: (X + 0.03191489362)(X + 0.03191489362) = 0.171231326435 Calculate the square root of the right side: 0.413801071 Break this problem into two subproblems by setting (X + 0.03191489362) equal to 0.413801071 and -0.413801071.Subproblem 1
X + 0.03191489362 = 0.413801071 Simplifying X + 0.03191489362 = 0.413801071 Reorder the terms: 0.03191489362 + X = 0.413801071 Solving 0.03191489362 + X = 0.413801071 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.03191489362' to each side of the equation. 0.03191489362 + -0.03191489362 + X = 0.413801071 + -0.03191489362 Combine like terms: 0.03191489362 + -0.03191489362 = 0.00000000000 0.00000000000 + X = 0.413801071 + -0.03191489362 X = 0.413801071 + -0.03191489362 Combine like terms: 0.413801071 + -0.03191489362 = 0.38188617738 X = 0.38188617738 Simplifying X = 0.38188617738Subproblem 2
X + 0.03191489362 = -0.413801071 Simplifying X + 0.03191489362 = -0.413801071 Reorder the terms: 0.03191489362 + X = -0.413801071 Solving 0.03191489362 + X = -0.413801071 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.03191489362' to each side of the equation. 0.03191489362 + -0.03191489362 + X = -0.413801071 + -0.03191489362 Combine like terms: 0.03191489362 + -0.03191489362 = 0.00000000000 0.00000000000 + X = -0.413801071 + -0.03191489362 X = -0.413801071 + -0.03191489362 Combine like terms: -0.413801071 + -0.03191489362 = -0.44571596462 X = -0.44571596462 Simplifying X = -0.44571596462Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.38188617738, -0.44571596462}
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